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From: <sla...@us...> - 2012-03-20 02:03:44
|
Revision: 9973
http://octave.svn.sourceforge.net/octave/?rev=9973&view=rev
Author: slackydeb
Date: 2012-03-20 02:03:37 +0000 (Tue, 20 Mar 2012)
Log Message:
-----------
ga: add devel folder
Thanks to Carn?\195?\171 Draug for clarification on package dirs
structure.
Reference:
http://octave.svn.sourceforge.net/viewvc/octave/trunk/octave-forge/main/control/devel/INFO?revision=7804&view=markup
Added Paths:
-----------
trunk/octave-forge/main/ga/devel/
trunk/octave-forge/main/ga/devel/INFO
Added: trunk/octave-forge/main/ga/devel/INFO
===================================================================
--- trunk/octave-forge/main/ga/devel/INFO (rev 0)
+++ trunk/octave-forge/main/ga/devel/INFO 2012-03-20 02:03:37 UTC (rev 9973)
@@ -0,0 +1,3 @@
+The folder "devel" and its content is ignored by "pkg install". The
+folder is intended for draft code and other stuff which is not
+suitable for "normal" users.
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
|
From: <mma...@us...> - 2012-03-19 21:31:54
|
Revision: 9972
http://octave.svn.sourceforge.net/octave/?rev=9972&view=rev
Author: mmarzolla
Date: 2012-03-19 21:31:47 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
new example in documentation
Modified Paths:
--------------
trunk/octave-forge/main/queueing/doc/markovchains.txi
trunk/octave-forge/main/queueing/inst/dtmc.m
trunk/octave-forge/main/queueing/inst/dtmc_fpt.m
trunk/octave-forge/main/queueing/inst/dtmc_mtta.m
Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-19 16:31:21 UTC (rev 9971)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-19 21:31:47 UTC (rev 9972)
@@ -140,12 +140,79 @@
@noindent @strong{EXAMPLE}
+This example is from [GrSn97]. Let us consider a maze with nine rooms,
+as shown in the following figure
+
@example
@group
-@verbatiminclude @value{top_srcdir}/examples/demo_1_dtmc.m
++-----+-----+-----+
+| | | |
+| 1 2 3 |
+| | | |
++- -+- -+- -+
+| | | |
+| 4 5 6 |
+| | | |
++- -+- -+- -+
+| | | |
+| 7 8 9 |
+| | | |
++-----+-----+-----+
@end group
@end example
+A mouse is placed in one of the rooms and can wander around. At each
+step, the mouse moves to one of the neighboring rooms with equal
+probability: if it is in room 1, it van move to room 2 and 4 with
+probability 1/2. If the mouse is in room 8, it can move to either 7, 5
+or 9 with probability 1/3.
+
+The transition probability @math{\bf P} from room @math{i} to room
+@math{j} is the following:
+
+@iftex
+@tex
+$$ {\bf P} =
+\pmatrix{ 0 & 1/2 & 0 & 1/2 & 0 & 0 & 0 & 0 & 0 \cr
+ 1/3 & 0 & 1/3 & 0 & 1/3 & 0 & 0 & 0 & 0 \cr
+ 0 & 1/2 & 0 & 0 & 0 & 1/2 & 0 & 0 & 0 \cr
+ 1/3 & 0 & 0 & 0 & 1/3 & 0 & 1/3 & 0 & 0 \cr
+ 0 & 1/4 & 0 & 1/4 & 0 & 1/4 & 0 & 1/4 & 0 \cr
+ 0 & 0 & 1/3 & 0 & 1/3 & 0 & 0 & 0 & 1/3 \cr
+ 0 & 0 & 0 & 1/2 & 0 & 0 & 0 & 1/2 & 0 \cr
+ 0 & 0 & 0 & 0 & 1/3 & 0 & 1/3 & 0 & 1/3 \cr
+ 0 & 0 & 0 & 0 & 0 & 1/2 & 0 & 1/2 & 0 }
+$$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+ / 0 1/2 0 1/2 0 0 0 0 0 \
+ | 1/3 0 1/3 0 1/3 0 0 0 0 |
+ | 0 1/2 0 0 0 1/2 0 0 0 |
+ | 1/3 0 0 0 1/3 0 1/3 0 0 |
+ P = | 0 1/4 0 1/4 0 1/4 0 1/4 0 |
+ | 0 0 1/3 0 1/3 0 0 0 1/3 |
+ | 0 0 0 1/2 0 0 0 1/2 0 |
+ | 0 0 0 0 1/3 0 1/3 0 1/3 |
+ \ 0 0 0 0 0 1/2 0 1/2 0 /
+@end group
+@end example
+@end ifnottex
+
+The stationary state occupancy probability vector can be computed
+using the following code:
+
+@example
+@c @group
+@verbatiminclude @value{top_srcdir}/examples/demo_1_dtmc.m
+@c @end group
+ @result{} 0.083333 0.125000 0.083333 0.125000
+ 0.166667 0.125000 0.083333 0.125000
+ 0.083333
+@end example
+
@c
@node Birth-death process (DTMC)
@subsection Birth-death process
@@ -325,6 +392,30 @@
@end example
@end ifnottex
+According to the definition above, @math{M_{i,i} = 0}. We arbitrarily
+redefine @math{M_{i,i}} to be the @emph{mean recurrence time}
+@math{r_i} for state @math{i}, that is the average number of
+transitions needed to return to state @math{i} starting from
+it. @math{r_i} is defined as:
+
+@iftex
+@tex
+$$ r_i = {1 \over \pi_i} $$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+ 1
+r_i = -----
+ \pi_i
+@end group
+@end example
+@end ifnottex
+
+@noindent where @math{\pi_i} is the stationary probability of visiting state
+@math{i}.
+
@DOCSTRING(dtmc_fpt)
@c
Modified: trunk/octave-forge/main/queueing/inst/dtmc.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc.m 2012-03-19 16:31:21 UTC (rev 9971)
+++ trunk/octave-forge/main/queueing/inst/dtmc.m 2012-03-19 21:31:47 UTC (rev 9972)
@@ -156,7 +156,36 @@
%! p = dtmc(P);
%! assert( p, [.0625 .25 .375 .25 .0625], 10*eps );
+## "Rat maze" problem (p. 441 of [GrSn97]);
+%!test
+%! P = zeros(9,9);
+%! P(1,[2 4]) = 1/2;
+%! P(2,[1 5 3]) = 1/3;
+%! P(3,[2 6]) = 1/2;
+%! P(4,[1 5 7]) = 1/3;
+%! P(5,[2 4 6 8]) = 1/4;
+%! P(6,[3 5 9]) = 1/3;
+%! P(7,[4 8]) = 1/2;
+%! P(8,[7 5 9]) = 1/3;
+%! P(9,[6 8]) = 1/2;
+%! p = dtmc(P);
+%! assert( p, [1/12 1/8 1/12 1/8 1/6 1/8 1/12 1/8 1/12], 10*eps );
+
%!demo
+%! P = zeros(9,9);
+%! P(1,[2 4] ) = 1/2;
+%! P(2,[1 5 3] ) = 1/3;
+%! P(3,[2 6] ) = 1/2;
+%! P(4,[1 5 7] ) = 1/3;
+%! P(5,[2 4 6 8]) = 1/4;
+%! P(6,[3 5 9] ) = 1/3;
+%! P(7,[4 8] ) = 1/2;
+%! P(8,[7 5 9] ) = 1/3;
+%! P(9,[6 8] ) = 1/2;
+%! p = dtmc(P);
+%! disp(p)
+
+%!demo
%! a = 0.2;
%! b = 0.15;
%! P = [ 1-a a; b 1-b];
Modified: trunk/octave-forge/main/queueing/inst/dtmc_fpt.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc_fpt.m 2012-03-19 16:31:21 UTC (rev 9971)
+++ trunk/octave-forge/main/queueing/inst/dtmc_fpt.m 2012-03-19 21:31:47 UTC (rev 9972)
@@ -73,8 +73,7 @@
error("Cannot compute first passage times for absorbing chains");
endif
- ## Source:
- ## http://www.cs.virginia.edu/~gfx/Courses/2006/DataDriven/bib/texsyn/Chapter11.pdf
+ ## Source [GrSn97]
w = dtmc(P); # steady state probability vector
W = repmat(w,N,1);
## Z = (I - P + W)^-1 where W is the matrix where each row is the
@@ -100,8 +99,7 @@
%! M = dtmc_fpt(P);
%! assert( diag(M)', 1./p, 1e-8 );
-## Example on p. 461 of
-## http://www.cs.virginia.edu/~gfx/Courses/2006/DataDriven/bib/texsyn/Chapter11.pdf
+## Example on p. 461 of [GrSn97]
%!test
%! P = [ 0 1 0 0 0; \
%! .25 .0 .75 0 0; \
@@ -127,6 +125,21 @@
%! endfor
%! endfor
+## "Rat maze" problem (p. 453 of [GrSn97]);
+%!test
+%! P = zeros(9,9);
+%! P(1,[2 4]) = .5;
+%! P(2,[1 5 3]) = 1/3;
+%! P(3,[2 6]) = .5;
+%! P(4,[1 5 7]) = 1/3;
+%! P(5,[2 4 6 8]) = 1/4;
+%! P(6,[3 5 9]) = 1/3;
+%! P(7,[4 8]) = .5;
+%! P(8,[7 5 9]) = 1/3;
+%! P(9,[6 8]) = .5;
+%! M = dtmc_fpt(P);
+%! assert( M(1:9 != 5,5)', [6 5 6 5 5 6 5 6], 10*eps );
+
%!demo
%! P = [ 0.0 0.9 0.1; \
%! 0.1 0.0 0.9; \
Modified: trunk/octave-forge/main/queueing/inst/dtmc_mtta.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc_mtta.m 2012-03-19 16:31:21 UTC (rev 9971)
+++ trunk/octave-forge/main/queueing/inst/dtmc_mtta.m 2012-03-19 21:31:47 UTC (rev 9972)
@@ -112,8 +112,8 @@
## Source: Grinstead, Charles M.; Snell, J. Laurie (July 1997). "Ch.
## 11: Markov Chains". Introduction to Probability. American
## Mathematical Society. ISBN 978-0821807491.
+ ## http://www.cs.virginia.edu/~gfx/Courses/2006/DataDriven/bib/texsyn/Chapter11.pdf
- ## http://www.cs.virginia.edu/~gfx/Courses/2006/DataDriven/bib/texsyn/Chapter11.pdf
tmpN = inv(eye(k) - P(tr,tr)); # matrix N = (I-Q)^-1
N(tr,tr) = tmpN;
R = P(tr,ab);
@@ -154,8 +154,7 @@
%! assert( B(3,1), 0.5, 10*eps );
%! assert( B(3,5), 0.5, 10*eps );
-## Example on p. 422 of
-## http://www.cs.virginia.edu/~gfx/Courses/2006/DataDriven/bib/texsyn/Chapter11.pdf
+## Example on p. 422 of [GrSn97]
%!test
%! P = dtmc_bd([0 .5 .5 .5 .5], [.5 .5 .5 .5 0]);
%! [t N B] = dtmc_mtta(P);
@@ -230,3 +229,19 @@
%! text(f*1.1,0.2,["Mean Time to Absorption (" num2str(f) ")"]);
%! xlabel("Step number (n)");
%! title("Probability of finishing the game before step n");
+
+## "Rat maze" problem (p. 453 of [GrSn97]);
+%!test
+%! P = zeros(9,9);
+%! P(1,[2 4]) = .5;
+%! P(2,[1 5 3]) = 1/3;
+%! P(3,[2 6]) = .5;
+%! P(4,[1 5 7]) = 1/3;
+%! P(5,:) = 0; P(5,5) = 1;
+%! P(6,[3 5 9]) = 1/3;
+%! P(7,[4 8]) = .5;
+%! P(8,[7 5 9]) = 1/3;
+%! P(9,[6 8]) = .5;
+%! t = dtmc_mtta(P);
+%! assert( t, [6 5 6 5 0 5 6 5 6], 10*eps );
+
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
|
From: <mma...@us...> - 2012-03-19 16:31:30
|
Revision: 9971
http://octave.svn.sourceforge.net/octave/?rev=9971&view=rev
Author: mmarzolla
Date: 2012-03-19 16:31:21 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
bug fix in the examples
Modified Paths:
--------------
trunk/octave-forge/main/queueing/inst/ctmc_exps.m
Modified: trunk/octave-forge/main/queueing/inst/ctmc_exps.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc_exps.m 2012-03-19 16:16:49 UTC (rev 9970)
+++ trunk/octave-forge/main/queueing/inst/ctmc_exps.m 2012-03-19 16:31:21 UTC (rev 9971)
@@ -152,10 +152,9 @@
%!demo
%! lambda = 0.5;
%! N = 4;
-%! birth = lambda*linspace(1,N-1,N-1);
-%! death = zeros(1,N-1);
-%! Q = diag(birth,1)+diag(death,-1);
-%! Q -= diag(sum(Q,2));
+%! b = lambda*[1:N-1];
+%! d = zeros(size(b));
+%! Q = ctmc_bd(b,d);
%! t = linspace(0,10,100);
%! p0 = zeros(1,N); p0(1)=1;
%! L = zeros(length(t),N);
@@ -173,10 +172,9 @@
%!demo
%! lambda = 0.5;
%! N = 4;
-%! birth = lambda*linspace(1,N-1,N-1);
-%! death = 0*birth;
-%! Q = diag(birth,1)+diag(death,-1);
-%! Q -= diag(sum(Q,2));
+%! b = lambda*[1:N-1];
+%! d = zeros(size(b));
+%! Q = ctmc_bd(b,d);
%! p0 = zeros(1,N); p0(1)=1;
%! L = ctmc_exps(Q,p0);
%! disp(L);
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
|
From: <par...@us...> - 2012-03-19 16:16:58
|
Revision: 9970
http://octave.svn.sourceforge.net/octave/?rev=9970&view=rev
Author: paramaniac
Date: 2012-03-19 16:16:49 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
control-devel: calculate initial state vector
Modified Paths:
--------------
trunk/octave-forge/extra/control-devel/devel/test_slident.m
trunk/octave-forge/extra/control-devel/src/slident.cc
Modified: trunk/octave-forge/extra/control-devel/devel/test_slident.m
===================================================================
--- trunk/octave-forge/extra/control-devel/devel/test_slident.m 2012-03-19 15:35:53 UTC (rev 9969)
+++ trunk/octave-forge/extra/control-devel/devel/test_slident.m 2012-03-19 16:16:49 UTC (rev 9970)
@@ -2031,7 +2031,7 @@
rcond = 0.0;
tol = -1.0;
-[a, b, c, d, q, ry, s, k] = slident (Y, U, nobr, meth, alg, jobd, batch, conct, ctrl, rcond, tol)
+[a, b, c, d, q, ry, s, k, x0] = slident (Y, U, nobr, meth, alg, jobd, batch, conct, ctrl, rcond, tol)
ae = [ 0.8924 0.3887 0.1285 0.1716
@@ -2077,23 +2077,27 @@
-figure (1)
-plot (Y)
+% figure (1)
+% plot (Y)
P = ss (a, b, c, d, 1);
-figure (2)
-lsim (P, U)
-%lsim (P, U, [], x0) % initial values dependent on realization, IB01BD != IB01CD
+% figure (2)
+% lsim (P, U)
+% lsim (P, U, [], x0) % initial values dependent on realization, IB01BD != IB01CD
-[y, t] = lsim (P, U);
+% [y, t] = lsim (P, U);
+[y, t] = lsim (P, U, [], x0);
+
figure (3)
plot (t, Y, 'b', t, y, 'r')
legend ('y measured', 'y simulated', 'location', 'southeast')
-axis tight
+%axis tight
+% print -depsc2 ident.eps
+
%n
%sv
Modified: trunk/octave-forge/extra/control-devel/src/slident.cc
===================================================================
--- trunk/octave-forge/extra/control-devel/src/slident.cc 2012-03-19 15:35:53 UTC (rev 9969)
+++ trunk/octave-forge/extra/control-devel/src/slident.cc 2012-03-19 16:16:49 UTC (rev 9970)
@@ -561,7 +561,6 @@
// ldwork = max (ldwork_a, ldwork_b, ldwork_c)
-/*
// arguments in
char jobx0 = 'X';
char comuse = 'U';
@@ -571,57 +570,19 @@
int ldv = max (1, n);
ColumnVector x0 (n);
- Matrix (ldv, n);
+ Matrix v (ldv, n);
// workspace
int liwork_c = n; // if JOBX0 = 'X' and COMUSE <> 'C'
int ldwork_c;
-
- ldwork_c = ldw1 + n*( n + m + l ) + max (5*n, ldw1, min (ldw2, ldw3))
-
-
- // I can't find a definition for parameter 't'
-
-C The length of the array DWORK.
-C LDWORK >= 2, if JOBX0 = 'N' and COMUSE <> 'C', or
-C if max( N, M ) = 0.
-C Otherwise,
-C LDWORK >= LDW1 + N*( N + M + L ) +
-C max( 5*N, LDW1, min( LDW2, LDW3 ) ),
-C where, if COMUSE = 'C', then
-C LDW1 = 2, if M = 0 or JOB = 'B',
-C LDW1 = 3, if M > 0 and JOB = 'D',
-C LDWa = t*L*(r + 1) + max( N + max( d, f ), 6*r ),
-C LDW2 = LDWa, if M = 0 or JOB = 'B',
-C LDW2 = max( LDWa, t*L*(r + 1) + 2*M*M + 6*M ),
-C if M > 0 and JOB = 'D',
-C LDWb = (b + r)*(r + 1) +
-C max( q*(r + 1) + N*N*M + c + max( d, f ), 6*r ),
-C LDW3 = LDWb, if M = 0 or JOB = 'B',
-C LDW3 = max( LDWb, (b + r)*(r + 1) + 2*M*M + 6*M ),
-C if M > 0 and JOB = 'D',
-C r = N*M + a,
-C a = 0, if JOBX0 = 'N',
-C a = N, if JOBX0 = 'X';
-C b = 0, if JOB = 'B',
-C b = L*M, if JOB = 'D';
-C c = 0, if JOBX0 = 'N',
-C c = L*N, if JOBX0 = 'X';
-C d = 0, if JOBX0 = 'N',
-C d = 2*N*N + N, if JOBX0 = 'X';
-C f = 2*r, if JOB = 'B' or M = 0,
-C f = M + max( 2*r, M ), if JOB = 'D' and M > 0;
-C q = b + r*L;
-C and, if JOBX0 = 'X' and COMUSE <> 'C', then
-C LDW1 = 2,
-C LDW2 = t*L*(N + 1) + 2*N + max( 2*N*N, 4*N ),
-C LDW3 = N*(N + 1) + 2*N + max( q*(N + 1) + 2*N*N + L*N,
-C 4*N ),
-C q = N*L.
-C For good performance, LDWORK should be larger.
+ int t = nsmp;
+
+ int ldw1_c = 2;
+ int ldw2_c = t*l*(n + 1) + 2*n + max (2*n*n, 4*n);
+ int ldw3_c = n*(n + 1) + 2*n + max (n*l*(n + 1) + 2*n*n + l*n, 4*n);
+ ldwork_c = ldw1_c + n*( n + m + l ) + max (5*n, ldw1_c, min (ldw2_c, ldw3_c));
-
OCTAVE_LOCAL_BUFFER (int, iwork_c, liwork_c);
OCTAVE_LOCAL_BUFFER (double, dwork_c, ldwork_c);
@@ -632,7 +593,7 @@
// SLICOT routine IB01CD
F77_XFCN (ib01cd, IB01CD,
- (jobx0, comuse, job***,
+ (jobx0, comuse, jobbd,
n, m, l,
nsmp,
a.fortran_vec (), lda,
@@ -676,7 +637,7 @@
error_msg ("ident", info_c, 2, err_msg_c);
warning_msg ("ident", iwarn_c, 6, warn_msg_c);
-*/
+
// return values
retval(0) = a;
@@ -689,7 +650,7 @@
retval(6) = s;
retval(7) = k;
- //retval(8) = x0;
+ retval(8) = x0;
//retval(0) = octave_value (n);
//retval(1) = r;
//retval(2) = sv;
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|
|
From: <mma...@us...> - 2012-03-19 15:36:04
|
Revision: 9969
http://octave.svn.sourceforge.net/octave/?rev=9969&view=rev
Author: mmarzolla
Date: 2012-03-19 15:35:53 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
improved documentation
Modified Paths:
--------------
trunk/octave-forge/main/queueing/doc/markovchains.txi
Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-19 12:27:55 UTC (rev 9968)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-19 15:35:53 UTC (rev 9969)
@@ -84,13 +84,13 @@
We denote with @math{{\bf \pi}(n) = \left(\pi_1(n), \pi_2(n), @dots{},
\pi_N(n) \right)} the @emph{state occupancy probability vector} at step
@math{n}. @math{\pi_i(n)} denotes the probability that the system is
-in state @math{i} at step @math{n}.
+in state @math{i} after @math{n} transitions.
Given the transition probability matrix @math{\bf P} and the initial
-state occupancy probability vector @math{{\bf \pi}(0) = \left(\pi_1(0),
-\pi_2(0), @dots{}, \pi_N(0)\right)} at step 0, the state occupancy
-probability vector @math{{\bf \pi}(n)} at step @math{n} can be
-computed as:
+state occupancy probability vector @math{{\bf \pi}(0) =
+\left(\pi_1(0), \pi_2(0), @dots{}, \pi_N(0)\right)}, the state
+occupancy probabilities @math{{\bf \pi}(n)} after @math{n} transitions
+can easily be computed as:
@iftex
@tex
@@ -107,11 +107,34 @@
Under certain conditions, there exists a @emph{stationary state
occupancy probability} @math{{\bf \pi} = \lim_{n \rightarrow +\infty}
-{\bf \pi}(n)}, which is independent from the initial state occupancy
-@math{{\bf \pi}(0)}. The stationary state occupancy probability vector
-@math{\bf \pi} satisfies @math{{\bf \pi} = {\bf \pi} {\bf P}}
-and @math{\sum_{i=1}^N \pi_i = 1}
+{\bf \pi}(n)}, which is independent from the initial occupancy
+@math{{\bf \pi}(0)}. The stationary vector @math{\bf \pi} can be
+computed as the solution of the following linear system:
+@iftex
+@tex
+$$
+\left\{ \eqalign{
+{\bf \pi P} & = {\bf \pi} \cr
+{\bf \pi 1}^T & = 1
+} \right.
+$$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+/
+| \pi P = \pi
+| \pi 1^T = 1
+\
+@end group
+@end example
+@end ifnottex
+
+@noindent where @math{\bf 1} is the row vector of ones, and @math{( \cdot )^T}
+the transpose operator.
+
@c
@DOCSTRING(dtmc)
@@ -137,7 +160,7 @@
matrix @math{\bf P} and an integer @math{n @geq{} 0}, we let
@math{L_i(n)} be the the expected number of visits to state @math{i}
during the first @math{n} transitions. The vector @math{{\bf L}(n) =
-( L_1(n), L_2(n), @dots{}, L_N(n) )} is defined as:
+( L_1(n), L_2(n), @dots{}, L_N(n) )} is defined as
@iftex
@tex
@@ -179,17 +202,15 @@
@end example
@end ifnottex
-@noindent where we suppose that the first @math{t} states are transient
-and the last @math{r} states are absorbing.
+@noindent where the first @math{t} states are transient
+and the last @math{r} states are absorbing. The matrix @math{{\bf N} =
+({\bf I} - {\bf Q})^{-1}} is called the @emph{fundamental matrix};
+@math{N(i,j)} represents the expected number of times that the process
+is in the @math{j}-th transient state if it is started in the
+@math{i}-th transient state. If we reshape @math{\bf N} to the size of
+@math{\bf P} (filling missing entries with zeros), we have that, for
+absorbing chains @math{{\bf L} = {\bf \pi}(0){\bf N}}.
-The matrix @math{{\bf N} = ({\bf I} - {\bf Q})^{-1}} is called the
-@emph{fundamental matrix}; @math{N(i,j)} represents the expected
-number of times that the process is in the @math{j}-th transient state
-if it is started in the @math{i}-th transient state. If we reshape
-@math{\bf N} to the size of @math{\bf P} (filling missing entries with
-zeros), we have that, for absorbing chains @math{{\bf L} = {\bf
-\pi}(0){\bf N}}.
-
@DOCSTRING(dtmc_exps)
@c
@@ -202,6 +223,43 @@
@node Mean time to absorption (DTMC)
@subsection Mean Time to Absorption
+The @emph{mean time to absorption} is defined as the average number of
+transitions which are required to reach an absorbing state, starting
+from a transient state (or given an initial state occupancy
+probability vector @math{{\bf \pi}(0)} ).
+
+Let @math{{\bf t}_i} be the expected number of steps before being
+absorbed in any absorbing state, starting from state @math{i}. Vector
+@math{\bf t} can be easiliy computed from the fundamental matrix
+@math{\bf N} (@pxref{Expected number of visits (DTMC)}) as
+
+@iftex
+@tex
+$$ {\bf t} = {\bf 1 N} $$
+@end tex
+@end iftex
+@ifnottex
+@example
+t = 1 N
+@end example
+@end ifnottex
+
+We can define a matrix @math{{\bf B} = [ B_{i, j} ]} such that
+@math{B_{i, j}} is the probability of being absorbed in state
+@math{j}, starting from transient state @math{i}. Again, using
+the fundamental matrix @math{\bf N} and @math{\bf R}, we have
+
+@iftex
+@tex
+$$ {\bf B} = {\bf N R} $$
+@end tex
+@end iftex
+@ifnottex
+@example
+B = N R
+@end example
+@end ifnottex
+
@DOCSTRING(dtmc_mtta)
@c
@@ -230,6 +288,43 @@
@end example
@end ifnottex
+To compute @math{{\bf M} = [ M_{i, j}]} a different formulation is
+used. Let @math{\bf W} be the @math{N \times N} matrix having each
+row equal to the steady-state probability vector @math{\bf \pi} for
+@math{\bf P}; let @math{\bf I} be the @math{N \times N} identity
+matrix. Define matrix @math{\bf Z} as follows:
+
+@iftex
+@tex
+$$ {\bf Z} = \left( {\bf I} - {\bf P} + {\bf W} \right)^{-1} $$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+ -1
+Z = (I - P + W)
+@end group
+@end example
+@end ifnottex
+
+@noindent Then, we have that
+
+@iftex
+@tex
+$$ M_{i, j} = {Z_{j, j} - Z_{i, j} \over \pi_j} $$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+ Z_jj - Z_ij
+M_ij = -----------
+ \pi_j
+@end group
+@end example
+@end ifnottex
+
@DOCSTRING(dtmc_fpt)
@c
@@ -303,9 +398,30 @@
@emph{stationary state occupancy probability} @math{{\bf \pi} =
\lim_{t \rightarrow +\infty} {\bf \pi}(t)}, which is independent from
the initial state occupancy @math{{\bf \pi}(0)}. The stationary state
-occupancy probability vector @math{\bf \pi} satisfies
-@math{{\bf \pi} {\bf Q} = {\bf 0}} and @math{\sum_{i=1}^N \pi_i = 1}.
+occupancy probability vector @math{\bf \pi} can be computed as the
+solution of the following linear system:
+@iftex
+@tex
+$$
+\left\{ \eqalign{
+{\bf \pi Q} & = {\bf 0} \cr
+{\bf \pi 1}^T & = 1
+} \right.
+$$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+/
+| \pi Q = 0
+| \pi 1^T = 1
+\
+@end group
+@end example
+@end ifnottex
+
@DOCSTRING(ctmc)
@noindent @strong{EXAMPLE}
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|
|
From: <mma...@us...> - 2012-03-19 12:28:05
|
Revision: 9968
http://octave.svn.sourceforge.net/octave/?rev=9968&view=rev
Author: mmarzolla
Date: 2012-03-19 12:27:55 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
documentation improvements
Modified Paths:
--------------
trunk/octave-forge/main/queueing/doc/markovchains.txi
trunk/octave-forge/main/queueing/inst/ctmc_bd.m
trunk/octave-forge/main/queueing/inst/dtmc_bd.m
Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-19 09:34:32 UTC (rev 9967)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-19 12:27:55 UTC (rev 9968)
@@ -39,7 +39,8 @@
@iftex
@tex
-$$P\left(X_{n+1} = x_{n+1}\ |\ X_n = x_n, X_{n-1} = x_{n-1}, \ldots, X_0 = x_0 \right) = P\left(X_{n+1} = x_{n+1}\ |\ X_n = x_n\right)$$
+$$\eqalign{P\left(X_{n+1} = x_{n+1}\ |\ X_n = x_n, X_{n-1} = x_{n-1}, \ldots, X_0 = x_0 \right) \cr
+& = P\left(X_{n+1} = x_{n+1}\ |\ X_n = x_n\right)}$$
@end tex
@end iftex
@ifnottex
@@ -52,10 +53,10 @@
The evolution of a Markov chain with finite state space @math{@{1, 2,
@dots{}, N@}} can be fully described by a stochastic matrix @math{{\bf
-P}(n) = P_{i,j}(n)} such that @math{P_{i, j}(n) = P( X_{n+1} = j\ |\
+P}(n) = [ P_{i,j}(n) ]} such that @math{P_{i, j}(n) = P( X_{n+1} = j\ |\
X_n = i )}. If the Markov chain is homogeneous (that is, the
transition probability matrix @math{{\bf P}(n)} is time-independent),
-we can simply write @math{{\bf P} = P_{i, j}}, where @math{P_{i, j} =
+we can simply write @math{{\bf P} = [P_{i, j}]}, where @math{P_{i, j} =
P( X_{n+1} = j\ |\ X_n = i )} for all @math{n=0, 1, @dots{}}.
The transition probability matrix @math{\bf P} must satisfy the
@@ -244,7 +245,8 @@
@iftex
@tex
-$$P(X_{t_{n+1}} = x_{n+1}\ |\ X(t_n) = x_n, X(t_{n-1}) = x_{n-1}, \ldots, X(t_0) = x_0) = P(X(t_{n+1}) = x_{n+1}\ |\ X(t_n) = x_n)$$
+$$\eqalign{P(X(t_{n+1}) = x_{n+1}\ |\ X(t_n) = x_n, X(t_{n-1}) = x_{n-1}, \ldots, X(t_0) = x_0) \cr
+&= P(X(t_{n+1}) = x_{n+1}\ |\ X(t_n) = x_n)}$$
@end tex
@end iftex
@ifnottex
@@ -255,8 +257,9 @@
@emph{infinitesimal generator matrix} @math{{\bf Q} = [Q_{i,j}]} such
that for each @math{i \neq j}, @math{Q_{i, j}} is the transition rate
from state @math{i} to state @math{j}. The elements @math{Q_{i, i}}
-must be defined in such a way that the infinitesimal generator matrix
-@math{\bf Q} satisfies the property @math{\sum_{j=1}^N Q_{i, j} = 0}.
+qre defined as @math{Q_{i, i} = - \sum_{j \neq i} Q_{i, j}}, such that
+matrix @math{\bf Q} satisfies the property that, for all @math{i},
+@math{\sum_{j=1}^N Q_{i, j} = 0}.
@DOCSTRING(ctmc_check_Q)
@@ -373,8 +376,8 @@
@end ifnottex
@noindent where @math{{\bf \pi}(t) = {\bf \pi}(0) \exp({\bf Q}t)} is
-the state occupancy probability at time @math{t}; @math{\exp({\bf A})}
-is the matrix exponential of @math{\bf A}.
+the state occupancy probability at time @math{t}; @math{\exp({\bf Q}t)}
+is the matrix exponential of @math{{\bf Q}t}.
@DOCSTRING(ctmc_exps)
Modified: trunk/octave-forge/main/queueing/inst/ctmc_bd.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc_bd.m 2012-03-19 09:34:32 UTC (rev 9967)
+++ trunk/octave-forge/main/queueing/inst/ctmc_bd.m 2012-03-19 12:27:55 UTC (rev 9968)
@@ -17,37 +17,51 @@
## -*- texinfo -*-
##
-## @deftypefn {Function File} {@var{Q} =} ctmc_bd (@var{birth}, @var{death})
+## @deftypefn {Function File} {@var{Q} =} ctmc_bd (@var{b}, @var{d})
##
## @cindex Markov chain, continuous time
## @cindex Birth-death process
##
-## Returns the @math{N \times N} infinitesimal generator matrix @math{Q}
-## for a birth-death process with given rates.
+## Returns the infinitesimal generator matrix @math{Q} for a continuous
+## birth-death process over state space @math{1, 2, @dots{}, N}.
+## @code{@var{b}(i)} is the transition rate from state @math{i} to
+## @math{i+1}, and @code{@var{d}(i)} is the transition rate from state
+## @math{i+1} to state @math{i}, @math{i=1, 2, @dots{}, N-1}.
##
-## @strong{INPUTS}
+## Matrix @math{\bf Q} is therefore defined as:
##
-## @table @var
+## @iftex
+## @tex
+## $$ \pmatrix{ -\lambda_1 & \lambda_1 & & & & \cr
+## \mu_1 & -(\mu_1 + \lambda_2) & \lambda_2 & & \cr
+## & \mu_2 & -(\mu_2 + \lambda_3) & \lambda_3 & & \cr
+## \cr
+## & & \ddots & \ddots & \ddots & & \cr
+## \cr
+## & & & \mu_{N-2} & -(\mu_{N-2}+\lambda_{N-1}) & \lambda_{N-1} \cr
+## & & & & \mu_{N-1} & -\mu_{N-1} }
+## $$
+## @end tex
+## @noindent where @math{\lambda_i} and @math{\mu_i} are the birth and
+## death rates, respectively.
+## @end iftex
+## @ifnottex
+## @example
+## @group
+## / \
+## | -b(1) b(1) |
+## | d(1) -(d(1)+b(2)) b(2) |
+## | d(2) -(d(2)+b(3)) b(3) |
+## | |
+## | ... ... ... |
+## | |
+## | d(N-2) -(d(N-2)+b(N-1)) b(N-1) |
+## | d(N-1) -d(N-1) |
+## \ /
+## @end group
+## @end example
+## @end ifnottex
##
-## @item birth
-## Vector with @math{N-1} elements, where @code{@var{birth}(i)} is the
-## transition rate from state @math{i} to state @math{i+1}.
-##
-## @item death
-## Vector with @math{N-1} elements, where @code{@var{death}(i)} is the
-## transition rate from state @math{i+1} to state @math{i}.
-##
-## @end table
-##
-## @strong{OUTPUTS}
-##
-## @table @var
-##
-## @item Q
-## Infinitesimal generator matrix for the birth-death process.
-##
-## @end table
-##
## @end deftypefn
## Author: Moreno Marzolla <marzolla(at)cs.unibo.it>
Modified: trunk/octave-forge/main/queueing/inst/dtmc_bd.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc_bd.m 2012-03-19 09:34:32 UTC (rev 9967)
+++ trunk/octave-forge/main/queueing/inst/dtmc_bd.m 2012-03-19 12:27:55 UTC (rev 9968)
@@ -17,68 +17,83 @@
## -*- texinfo -*-
##
-## @deftypefn {Function File} {@var{P} =} dtmc_bd (@var{birth}, @var{death})
+## @deftypefn {Function File} {@var{P} =} dtmc_bd (@var{b}, @var{d})
##
## @cindex Markov chain, discrete time
## @cindex Birth-death process
##
-## Returns the @math{N \times N} transition probability matrix @math{P}
-## for a birth-death process with given rates.
+## Returns the transition probability matrix @math{P} for a discrete
+## birth-death process over state space @math{1, 2, @dots{}, N}.
+## @code{@var{b}(i)} is the transition probability from state
+## @math{i} to @math{i+1}, and @code{@var{d}(i)} is the transition
+## probability from state @math{i+1} to state @math{i}, @math{i=1, 2,
+## @dots{}, N-1}.
##
-## @strong{INPUTS}
+## Matrix @math{\bf P} is therefore defined as:
##
-## @table @var
+## @iftex
+## @tex
+## $$ \pmatrix{ (1-\lambda_1) & \lambda_1 & & & & \cr
+## \mu_1 & (1 - \mu_1 - \lambda_2) & \lambda_2 & & \cr
+## & \mu_2 & (1 - \mu_2 - \lambda_3) & \lambda_3 & & \cr
+## \cr
+## & & \ddots & \ddots & \ddots & & \cr
+## \cr
+## & & & \mu_{N-2} & (1 - \mu_{N-2}-\lambda_{N-1}) & \lambda_{N-1} \cr
+## & & & & \mu_{N-1} & (1-\mu_{N-1}) }
+## $$
+## @end tex
+## @noindent where @math{\lambda_i} and @math{\mu_i} are the birth and
+## death probabilities, respectively.
+## @end iftex
+## @ifnottex
+## @example
+## @group
+## / \
+## | 1-b(1) b(1) |
+## | d(1) (1-d(1)-b(2)) b(2) |
+## | d(2) (1-d(2)-b(3)) b(3) |
+## | |
+## | ... ... ... |
+## | |
+## | d(N-2) (1-d(N-2)-b(N-1)) b(N-1) |
+## | d(N-1) 1-d(N-1) |
+## \ /
+## @end group
+## @end example
+## @end ifnottex
##
-## @item birth
-## Vector with @math{N-1} elements, where @code{@var{birth}(i)} is the
-## transition probability from state @math{i} to state @math{i+1}.
-##
-## @item death
-## Vector with @math{N-1} elements, where @code{@var{death}(i)} is the
-## transition probability from state @math{i+1} to state @math{i}.
-##
-## @end table
-##
-## @strong{OUTPUTS}
-##
-## @table @var
-##
-## @item P
-## Transition probability matrix for the birth-death process.
-##
-## @end table
-##
## @end deftypefn
## Author: Moreno Marzolla <marzolla(at)cs.unibo.it>
## Web: http://www.moreno.marzolla.name/
-function P = dtmc_bd( birth, death )
+function P = dtmc_bd( b, d )
if ( nargin != 2 )
print_usage();
endif
- ( isvector( birth ) && isvector( death ) ) || \
+ ( isvector( b ) && isvector( d ) ) || \
usage( "birth and death must be vectors" );
- birth = birth(:); # make birth a column vector
- death = death(:); # make death a column vector
- size_equal( birth, death ) || \
+ b = b(:); # make b a column vector
+ d = d(:); # make d a column vector
+ size_equal( b, d ) || \
usage( "birth and death vectors must have the same length" );
- all( birth >= 0 ) || \
+ all( b >= 0 ) || \
usage( "birth probabilities must be >= 0" );
- all( death >= 0 ) || \
+ all( d >= 0 ) || \
usage( "death probabilities must be >= 0" );
- all( ([birth; 0] + [0; death]) <= 1 ) || \
- usage( "Inconsistent birth/death probabilities");
- ## builds the infinitesimal generator matrix
- P = diag( birth, 1 ) + diag( death, -1 );
+ all( ([b; 0] + [0; d]) <= 1 ) || \
+ usage( "d(i)+b(i+1) must be <= 1");
+
+ P = diag( b, 1 ) + diag( d, -1 );
P += diag( 1-sum(P,2) );
endfunction
%!test
%! birth = [.5 .5 .3];
%! death = [.6 .2 .3];
-%! fail("dtmc_bd(birth,death)","Inconsistent");
+%! fail("dtmc_bd(birth,death)","must be");
%!demo
%! birth = [ .2 .3 .4 ];
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
|
From: <jpi...@us...> - 2012-03-19 09:34:41
|
Revision: 9967
http://octave.svn.sourceforge.net/octave/?rev=9967&view=rev
Author: jpicarbajal
Date: 2012-03-19 09:34:32 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
geometry: further clenaing of PKG*
Modified Paths:
--------------
trunk/octave-forge/main/geometry/PKG_ADD
Modified: trunk/octave-forge/main/geometry/PKG_ADD
===================================================================
--- trunk/octave-forge/main/geometry/PKG_ADD 2012-03-19 09:33:33 UTC (rev 9966)
+++ trunk/octave-forge/main/geometry/PKG_ADD 2012-03-19 09:34:32 UTC (rev 9967)
@@ -12,7 +12,7 @@
arch = cstrcat (octave_config_info ("canonical_host_type"),
"-", octave_config_info ("api_version"));
if strcmp (arch , pp{end})
- dirname = [strcat(filesep(),{pp{1:end-1}}){:}]
+ dirname = [strcat(filesep(),{pp{1:end-1}}){:}];
pkg_folder = strsplit (pkg_folder,filesep (), true);
pkg_folder = [strcat(filesep(),{pkg_folder{1:end-1}}){:}];
end
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|
|
From: <jpi...@us...> - 2012-03-19 09:33:44
|
Revision: 9966
http://octave.svn.sourceforge.net/octave/?rev=9966&view=rev
Author: jpicarbajal
Date: 2012-03-19 09:33:33 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
geometry: further cleaning PKG*
Modified Paths:
--------------
trunk/octave-forge/main/geometry/PKG_ADD
trunk/octave-forge/main/geometry/PKG_DEL
Modified: trunk/octave-forge/main/geometry/PKG_ADD
===================================================================
--- trunk/octave-forge/main/geometry/PKG_ADD 2012-03-19 09:30:27 UTC (rev 9965)
+++ trunk/octave-forge/main/geometry/PKG_ADD 2012-03-19 09:33:33 UTC (rev 9966)
@@ -1,6 +1,6 @@
%1
dirlist = {"geom2d","io","polygons2d","shape2d","octclip", "graphs"};
-dirname = fileparts (canonicalize_file_name (mfilename ("fullpath")))
+dirname = fileparts (canonicalize_file_name (mfilename ("fullpath")));
pp = strsplit (dirname,filesep (), true);
%% Check if prefix was used
@@ -13,7 +13,6 @@
"-", octave_config_info ("api_version"));
if strcmp (arch , pp{end})
dirname = [strcat(filesep(),{pp{1:end-1}}){:}]
-% dirname = [pkg("prefix") filesep() pp{end-1}]
pkg_folder = strsplit (pkg_folder,filesep (), true);
pkg_folder = [strcat(filesep(),{pkg_folder{1:end-1}}){:}];
end
Modified: trunk/octave-forge/main/geometry/PKG_DEL
===================================================================
--- trunk/octave-forge/main/geometry/PKG_DEL 2012-03-19 09:30:27 UTC (rev 9965)
+++ trunk/octave-forge/main/geometry/PKG_DEL 2012-03-19 09:33:33 UTC (rev 9966)
@@ -13,7 +13,6 @@
"-", octave_config_info ("api_version"));
pp = strsplit (dirname,filesep (), true);
if strcmp(arch , pp{end})
- %dirname = [strcat(filesep(),{pp{1:end-1}}){:}]
dirname = [pkg("prefix") filesep() pp{end-1}];
pkg_folder = strsplit (pkg_folder,filesep (), true);
pkg_folder = [strcat(filesep(),{pkg_folder{1:end-1}}){:}];
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From: <jpi...@us...> - 2012-03-19 09:30:38
|
Revision: 9965
http://octave.svn.sourceforge.net/octave/?rev=9965&view=rev
Author: jpicarbajal
Date: 2012-03-19 09:30:27 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
geometry: removing keyboard from PKG*
Modified Paths:
--------------
trunk/octave-forge/main/geometry/PKG_ADD
trunk/octave-forge/main/geometry/PKG_DEL
Modified: trunk/octave-forge/main/geometry/PKG_ADD
===================================================================
--- trunk/octave-forge/main/geometry/PKG_ADD 2012-03-19 02:48:56 UTC (rev 9964)
+++ trunk/octave-forge/main/geometry/PKG_ADD 2012-03-19 09:30:27 UTC (rev 9965)
@@ -1,6 +1,6 @@
%1
dirlist = {"geom2d","io","polygons2d","shape2d","octclip", "graphs"};
-dirname = fileparts (canonicalize_file_name (mfilename ("fullpath")));
+dirname = fileparts (canonicalize_file_name (mfilename ("fullpath")))
pp = strsplit (dirname,filesep (), true);
%% Check if prefix was used
@@ -12,7 +12,8 @@
arch = cstrcat (octave_config_info ("canonical_host_type"),
"-", octave_config_info ("api_version"));
if strcmp (arch , pp{end})
- dirname = [strcat(filesep(),{pp{1:end-1}}){:}];
+ dirname = [strcat(filesep(),{pp{1:end-1}}){:}]
+% dirname = [pkg("prefix") filesep() pp{end-1}]
pkg_folder = strsplit (pkg_folder,filesep (), true);
pkg_folder = [strcat(filesep(),{pkg_folder{1:end-1}}){:}];
end
@@ -22,6 +23,7 @@
for ii=1:length (dirlist)
addpath ( [ pkg_folder filesep() dirlist{ii}],"-end")
endfor
+
else
%% Testing
warning("geometry:Devel","Adding path for testing.");
Modified: trunk/octave-forge/main/geometry/PKG_DEL
===================================================================
--- trunk/octave-forge/main/geometry/PKG_DEL 2012-03-19 02:48:56 UTC (rev 9964)
+++ trunk/octave-forge/main/geometry/PKG_DEL 2012-03-19 09:30:27 UTC (rev 9965)
@@ -13,7 +13,8 @@
"-", octave_config_info ("api_version"));
pp = strsplit (dirname,filesep (), true);
if strcmp(arch , pp{end})
- dirname = [strcat(filesep(),{pp{1:end-1}}){:}];
+ %dirname = [strcat(filesep(),{pp{1:end-1}}){:}]
+ dirname = [pkg("prefix") filesep() pp{end-1}];
pkg_folder = strsplit (pkg_folder,filesep (), true);
pkg_folder = [strcat(filesep(),{pkg_folder{1:end-1}}){:}];
end
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From: <car...@us...> - 2012-03-19 02:49:02
|
Revision: 9964
http://octave.svn.sourceforge.net/octave/?rev=9964&view=rev
Author: carandraug
Date: 2012-03-19 02:48:56 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
chk_spreadsheet_support: small syntax bugfix (missing comma)
Modified Paths:
--------------
trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m
Modified: trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m
===================================================================
--- trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m 2012-03-19 02:20:48 UTC (rev 9963)
+++ trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m 2012-03-19 02:48:56 UTC (rev 9964)
@@ -173,7 +173,7 @@
end %if
if (dbug), fprintf ('Java support OK\n'); end %if
catch
- error ('No Java support found: %s.' lasterr);
+ error ('No Java support found: %s.', lasterr);
end %try_catch
if (dbug), fprintf ('\nChecking javaclasspath for .jar class libraries needed for spreadsheet I/O...:\n'); end %if
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From: <car...@us...> - 2012-03-19 02:20:54
|
Revision: 9963
http://octave.svn.sourceforge.net/octave/?rev=9963&view=rev
Author: carandraug
Date: 2012-03-19 02:20:48 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
chk_spreadsheet_support: make error message more helpful on why java is failing
Modified Paths:
--------------
trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m
Modified: trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m
===================================================================
--- trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m 2012-03-19 00:54:13 UTC (rev 9962)
+++ trunk/octave-forge/main/io/inst/chk_spreadsheet_support.m 2012-03-19 02:20:48 UTC (rev 9963)
@@ -173,7 +173,7 @@
end %if
if (dbug), fprintf ('Java support OK\n'); end %if
catch
- error ('No Java support found.');
+ error ('No Java support found: %s.' lasterr);
end %try_catch
if (dbug), fprintf ('\nChecking javaclasspath for .jar class libraries needed for spreadsheet I/O...:\n'); end %if
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From: <sla...@us...> - 2012-03-19 00:54:19
|
Revision: 9962
http://octave.svn.sourceforge.net/octave/?rev=9962&view=rev
Author: slackydeb
Date: 2012-03-19 00:54:13 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: reduce number of generations in a test of ga
The high number of generations does not look strictly needed.
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/ga.m
Modified: trunk/octave-forge/main/ga/inst/ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:54:00 UTC (rev 9961)
+++ trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:54:13 UTC (rev 9962)
@@ -159,7 +159,7 @@
# TODO: structure/add tests below
-%!test x = ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("FitnessLimit", 1e-7, "Generations", 1000)));
+%!test x = ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("FitnessLimit", 1e-7, "Generations", 200)));
%!test x = ga (struct ("fitnessfcn", @(x) rastriginsfcn (x(1:2)) + ((x(3) ** 2) - (cos (2 * pi * x(3))) + 1) + (x(4) ** 2), "nvars", 4, "options", gaoptimset ("EliteCount", 5, "FitnessLimit", 1e-7, "PopInitRange", [-2; 2], "PopulationSize", 200)));
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From: <sla...@us...> - 2012-03-19 00:54:06
|
Revision: 9961
http://octave.svn.sourceforge.net/octave/?rev=9961&view=rev
Author: slackydeb
Date: 2012-03-19 00:54:00 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: polish unit tests of ga
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/ga.m
Modified: trunk/octave-forge/main/ga/inst/ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:41:01 UTC (rev 9960)
+++ trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:54:00 UTC (rev 9961)
@@ -157,6 +157,7 @@
%! "options", gaoptimset ());
%! x = ga (problem);
+# TODO: structure/add tests below
%!test x = ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("FitnessLimit", 1e-7, "Generations", 1000)));
@@ -187,4 +188,4 @@
%!test ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("Generations", 10, "Vectorized", "on")));
-%!xtest ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("Generations", 10, "UseParallel", "always")));
+%!#xtest ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("Generations", 10, "UseParallel", "always"))); TODO
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From: <sla...@us...> - 2012-03-19 00:41:07
|
Revision: 9960
http://octave.svn.sourceforge.net/octave/?rev=9960&view=rev
Author: slackydeb
Date: 2012-03-19 00:41:01 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: fix dummy demo
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/demo_ga.m
Modified: trunk/octave-forge/main/ga/inst/demo_ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/demo_ga.m 2012-03-19 00:34:25 UTC (rev 9959)
+++ trunk/octave-forge/main/ga/inst/demo_ga.m 2012-03-19 00:41:01 UTC (rev 9960)
@@ -21,9 +21,9 @@
## Author: Luca Favatella <sla...@gm...>
## Created: March 2012
-## Version: 0.0.3
+## Version: 0.0.4
-demo ga_demo
+demo demo_ga
%!demo
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From: <sla...@us...> - 2012-03-19 00:34:31
|
Revision: 9959
http://octave.svn.sourceforge.net/octave/?rev=9959&view=rev
Author: slackydeb
Date: 2012-03-19 00:34:25 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: polish code
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/ga.m
trunk/octave-forge/main/ga/inst/rastriginsfcn.m
Modified: trunk/octave-forge/main/ga/inst/ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:34:11 UTC (rev 9958)
+++ trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:34:25 UTC (rev 9959)
@@ -115,7 +115,7 @@
endfunction
-## number of arguments
+## number of input arguments
%!shared f, nvars
%! f = @rastriginsfcn;
%! nvars = 2;
@@ -125,8 +125,10 @@
%!error x = ga (f, nvars, [], [], [])
%!error x = ga (f, nvars, [], [], [], [], [])
%!error x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []], gaoptimset (), [])
-# TODO: test number of output arguments
+## number of output arguments
+# TODO
+
## type of arguments
# TODO
# TODO: test that each field in the user-specified "problem" structure is checked
Modified: trunk/octave-forge/main/ga/inst/rastriginsfcn.m
===================================================================
--- trunk/octave-forge/main/ga/inst/rastriginsfcn.m 2012-03-19 00:34:11 UTC (rev 9958)
+++ trunk/octave-forge/main/ga/inst/rastriginsfcn.m 2012-03-19 00:34:25 UTC (rev 9959)
@@ -34,9 +34,11 @@
endfunction
-## number of arguments
+## number of input arguments
%!error y = rastriginsfcn ()
%!error y = rastriginsfcn ([0, 0], "other argument")
+
+## number of output arguments
%!error [y1, y2] = rastriginsfcn ([0, 0])
## type of arguments
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From: <sla...@us...> - 2012-03-19 00:34:17
|
Revision: 9958
http://octave.svn.sourceforge.net/octave/?rev=9958&view=rev
Author: slackydeb
Date: 2012-03-19 00:34:11 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: polish gaoptimset
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/gaoptimset.m
Modified: trunk/octave-forge/main/ga/inst/gaoptimset.m
===================================================================
--- trunk/octave-forge/main/ga/inst/gaoptimset.m 2012-03-19 00:33:59 UTC (rev 9957)
+++ trunk/octave-forge/main/ga/inst/gaoptimset.m 2012-03-19 00:34:11 UTC (rev 9958)
@@ -21,7 +21,8 @@
## @strong{Inputs}
## @table @var
## @item param
-## Parameter to set. Unspecified parameters are set to their default values; specifying no parameters is allowed.
+## Parameter to set. Unspecified parameters are set to their default
+## values; specifying no parameters is allowed.
## @item value
## Value of @var{param}.
## @end table
@@ -60,7 +61,7 @@
## @end deftypefn
## Author: Luca Favatella <sla...@gm...>
-## Version: 4.4.6
+## Version: 4.4.7
function options = gaoptimset (varargin)
if ((nargout != 1) ||
@@ -86,21 +87,35 @@
endfunction
-%!error gaoptimset ("Generations", 123)
-%!error [a, b] = gaoptimset ("Generations", 123)
-
+## number of input arguments
%!error options = gaoptimset ("odd number of arguments")
%!error options = gaoptimset ("Generations", 123, "odd number of arguments")
+## number of output arguments
+%!error gaoptimset ("Generations", 123)
+%!error [a, b] = gaoptimset ("Generations", 123)
+## type of arguments
+# TODO
%!#error options = gaoptimset ("Vectorized", "bad value") # TODO: fix
%!#error options = gaoptimset ("UseParallel", "bad value") # TODO: fix
+# TODO: structure/add tests below
%!assert (getfield (gaoptimset ("Generations", 123), "Generations"), 123)
%!test
-%! options = gaoptimset ("EliteCount", 1, "FitnessLimit", 1e-7, "Generations", 1000, "PopInitRange", [-5; 5], "PopulationSize", 200);
+%! options = gaoptimset ("EliteCount", 1,
+%! "FitnessLimit", 1e-7,
+%! "Generations", 1000,
+%! "PopInitRange", [-5; 5],
+%! "PopulationSize", 200);
%!
%! ## "CrossoverFraction" is not specified, so gaoptimset should put the default value: testing this too
-%! assert ([(getfield (options, "CrossoverFraction")); (getfield (options, "EliteCount")); (getfield (options, "FitnessLimit")); (getfield (options, "Generations")); (getfield (options, "PopInitRange")); (getfield (options, "PopulationSize"))], [0.8; 1; 1e-7; 1000; [-5; 5]; 200])
\ No newline at end of file
+%! assert ([(getfield (options, "CrossoverFraction"));
+%! (getfield (options, "EliteCount"));
+%! (getfield (options, "FitnessLimit"));
+%! (getfield (options, "Generations"));
+%! (getfield (options, "PopInitRange"));
+%! (getfield (options, "PopulationSize"))],
+%! [0.8; 1; 1e-7; 1000; [-5; 5]; 200])
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From: <sla...@us...> - 2012-03-19 00:34:05
|
Revision: 9957
http://octave.svn.sourceforge.net/octave/?rev=9957&view=rev
Author: slackydeb
Date: 2012-03-19 00:33:59 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: add unit test for ga
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/ga.m
Modified: trunk/octave-forge/main/ga/inst/ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:33:47 UTC (rev 9956)
+++ trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:33:59 UTC (rev 9957)
@@ -129,6 +129,7 @@
## type of arguments
# TODO
+# TODO: test that each field in the user-specified "problem" structure is checked
## flawless execution with right arguments
%!shared f, nvars
@@ -148,7 +149,11 @@
%!test x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []]);
%!test x = ga (f, nvars, [], [], [], [], [], [], @nonlcon);
%!test x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []], gaoptimset ());
-# TODO: %!test x = ga (problem);
+%!test # TODO: convert to error after implementing private ga-specific createOptimProblem. All fields in the user-specified structure should be checked
+%! problem = struct ("fitnessfcn", @rastriginsfcn,
+%! "nvars", 2,
+%! "options", gaoptimset ());
+%! x = ga (problem);
%!test x = ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("FitnessLimit", 1e-7, "Generations", 1000)));
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From: <sla...@us...> - 2012-03-19 00:33:53
|
Revision: 9956
http://octave.svn.sourceforge.net/octave/?rev=9956&view=rev
Author: slackydeb
Date: 2012-03-19 00:33:47 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: add comments to ga unit tests
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/ga.m
Modified: trunk/octave-forge/main/ga/inst/ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:33:34 UTC (rev 9955)
+++ trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:33:47 UTC (rev 9956)
@@ -130,6 +130,7 @@
## type of arguments
# TODO
+## flawless execution with right arguments
%!shared f, nvars
%! f = @rastriginsfcn;
%! nvars = 2;
@@ -147,6 +148,7 @@
%!test x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []]);
%!test x = ga (f, nvars, [], [], [], [], [], [], @nonlcon);
%!test x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []], gaoptimset ());
+# TODO: %!test x = ga (problem);
%!test x = ga (struct ("fitnessfcn", @rastriginsfcn, "nvars", 2, "options", gaoptimset ("FitnessLimit", 1e-7, "Generations", 1000)));
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From: <sla...@us...> - 2012-03-19 00:33:41
|
Revision: 9955
http://octave.svn.sourceforge.net/octave/?rev=9955&view=rev
Author: slackydeb
Date: 2012-03-19 00:33:34 +0000 (Mon, 19 Mar 2012)
Log Message:
-----------
ga: add TODO comment
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/ga.m
Modified: trunk/octave-forge/main/ga/inst/ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/ga.m 2012-03-18 22:53:36 UTC (rev 9954)
+++ trunk/octave-forge/main/ga/inst/ga.m 2012-03-19 00:33:34 UTC (rev 9955)
@@ -125,6 +125,7 @@
%!error x = ga (f, nvars, [], [], [])
%!error x = ga (f, nvars, [], [], [], [], [])
%!error x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []], gaoptimset (), [])
+# TODO: test number of output arguments
## type of arguments
# TODO
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From: <cd...@us...> - 2012-03-18 22:53:42
|
Revision: 9954
http://octave.svn.sourceforge.net/octave/?rev=9954&view=rev
Author: cdf
Date: 2012-03-18 22:53:36 +0000 (Sun, 18 Mar 2012)
Log Message:
-----------
reduce randomness of test
Modified Paths:
--------------
trunk/octave-forge/extra/nurbs/inst/nrbbasisfun.m
Modified: trunk/octave-forge/extra/nurbs/inst/nrbbasisfun.m
===================================================================
--- trunk/octave-forge/extra/nurbs/inst/nrbbasisfun.m 2012-03-18 22:27:44 UTC (rev 9953)
+++ trunk/octave-forge/extra/nurbs/inst/nrbbasisfun.m 2012-03-18 22:53:36 UTC (rev 9954)
@@ -125,6 +125,8 @@
%! aux1 = linspace(0,1,m); aux2 = linspace(0,1,n);
%! nrb = nrbkntins (nrb, {aux1(2:end-1), aux2(2:end-1)});
%! u = rand (1, 30); v = rand (1, 10);
+%! u = u - min (u); u = u / max (u);
+%! v = v - min (v); v = v / max (v);
%! [B, N] = nrbbasisfun ({u, v}, nrb);
%! assert (sum(B, 2), ones(300, 1), 1e-6)
%! assert (all (all (B<=1)), true)
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From: <sla...@us...> - 2012-03-18 22:27:50
|
Revision: 9953
http://octave.svn.sourceforge.net/octave/?rev=9953&view=rev
Author: slackydeb
Date: 2012-03-18 22:27:44 +0000 (Sun, 18 Mar 2012)
Log Message:
-----------
ga: enable unit test for ga
Define test function without using "endfunction" in order to
support Octave 3.4.
Modified Paths:
--------------
trunk/octave-forge/main/ga/inst/ga.m
Modified: trunk/octave-forge/main/ga/inst/ga.m
===================================================================
--- trunk/octave-forge/main/ga/inst/ga.m 2012-03-18 22:20:41 UTC (rev 9952)
+++ trunk/octave-forge/main/ga/inst/ga.m 2012-03-18 22:27:44 UTC (rev 9953)
@@ -132,10 +132,9 @@
%!shared f, nvars
%! f = @rastriginsfcn;
%! nvars = 2;
-#%!function [C, Ceq] = nonlcon (x)
-#%! C = [];
-#%! Ceq = [];
-#%!endfunction
+%!function [C, Ceq] = nonlcon (x)
+%! C = [];
+%! Ceq = [];
%!test x = ga (f, nvars);
%!test x = ga (f, nvars, [], []);
%!test x = ga (f, nvars, ones (3, nvars), ones (3, 1));
@@ -145,7 +144,7 @@
%!test x = ga (f, nvars, [], [], [], [], - Inf (1, nvars), Inf (1, nvars));
%!test x = ga (f, nvars, [], [], [], [], - ones (1, nvars), ones (1, nvars));
%!test x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []]);
-#%!test x = ga (f, nvars, [], [], [], [], [], [], @nonlcon);
+%!test x = ga (f, nvars, [], [], [], [], [], [], @nonlcon);
%!test x = ga (f, nvars, [], [], [], [], [], [], @(x) [[], []], gaoptimset ());
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From: <prn...@us...> - 2012-03-18 22:20:48
|
Revision: 9952
http://octave.svn.sourceforge.net/octave/?rev=9952&view=rev
Author: prnienhuis
Date: 2012-03-18 22:20:41 +0000 (Sun, 18 Mar 2012)
Log Message:
-----------
Minor help text changes (get_first_help_sentence compatibility)
Modified Paths:
--------------
trunk/octave-forge/main/io/inst/object2json.m
Modified: trunk/octave-forge/main/io/inst/object2json.m
===================================================================
--- trunk/octave-forge/main/io/inst/object2json.m 2012-03-18 21:03:48 UTC (rev 9951)
+++ trunk/octave-forge/main/io/inst/object2json.m 2012-03-18 22:20:41 UTC (rev 9952)
@@ -22,7 +22,6 @@
function json = object2json (object)
- % function json = object2json (object)
% Returns a valid json string that will describe object; the string will
% be in a compact form (no spaces or line breaks).
%
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
|
From: <mma...@us...> - 2012-03-18 21:03:57
|
Revision: 9951
http://octave.svn.sourceforge.net/octave/?rev=9951&view=rev
Author: mmarzolla
Date: 2012-03-18 21:03:48 +0000 (Sun, 18 Mar 2012)
Log Message:
-----------
improvements to the documentation
Modified Paths:
--------------
trunk/octave-forge/main/queueing/doc/gettingstarted.txi
trunk/octave-forge/main/queueing/doc/markovchains.txi
trunk/octave-forge/main/queueing/doc/queueingnetworks.txi
trunk/octave-forge/main/queueing/doc/references.txi
trunk/octave-forge/main/queueing/inst/dtmc_taexps.m
trunk/octave-forge/main/queueing/inst/qnmarkov.m
Modified: trunk/octave-forge/main/queueing/doc/gettingstarted.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/gettingstarted.txi 2012-03-18 18:24:04 UTC (rev 9950)
+++ trunk/octave-forge/main/queueing/doc/gettingstarted.txi 2012-03-18 21:03:48 UTC (rev 9951)
@@ -51,7 +51,7 @@
routing of jobs within the network is described with a @emph{routing
probability matrix} @math{P}. Specifically, a request completing
service at center @math{i} is enqueued at center @math{j} with
-probability @math{P_{ij}}. Let us assume the following routing
+probability @math{P_{i, j}}. Let us assume the following routing
probability matrix:
@iftex
@@ -106,7 +106,7 @@
@iftex
@tex
$$
-V_j = \sum_{i=1}^K V_i P_{ij}
+V_j = \sum_{i=1}^K V_i P_{i, j}
$$
@end tex
@end iftex
@@ -117,7 +117,7 @@
@end ifnottex
We can compute @math{V_k} from the routing probability matrix
-@math{P_{ij}} using the @command{qnvisits} function:
+@math{P_{i, j}} using the @command{qnvisits} function:
@example
@group
@@ -250,7 +250,7 @@
@iftex
@tex
$$
-V_j = P_{0j} + \sum_{i=1}^K V_i P_{ij}
+V_j = P_{0, j} + \sum_{i=1}^K V_i P_{i, j}
$$
@end tex
@end iftex
@@ -260,12 +260,12 @@
@end example
@end ifnottex
-where @math{P_{0j}} is the probability of an external arrival to
+where @math{P_{0, j}} is the probability of an external arrival to
center @math{j}. This can be computed as:
@tex
$$
-P_{0j} = {\lambda_j \over \sum_{i=1}^K \lambda_i }
+P_{0, j} = {\lambda_j \over \sum_{i=1}^K \lambda_i }
$$
@end tex
Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-18 18:24:04 UTC (rev 9950)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-18 21:03:48 UTC (rev 9951)
@@ -39,7 +39,7 @@
@iftex
@tex
-$$P(X_{n+1} = x_{n+1}\ |\ X_n = x_n, X_{n-1} = x_{n-1}, \ldots, X_0 = x_0) = P(X_{n+1} = x_{n+1}\ |\ X_n = x_n)$$
+$$P\left(X_{n+1} = x_{n+1}\ |\ X_n = x_n, X_{n-1} = x_{n-1}, \ldots, X_0 = x_0 \right) = P\left(X_{n+1} = x_{n+1}\ |\ X_n = x_n\right)$$
@end tex
@end iftex
@ifnottex
@@ -56,7 +56,7 @@
X_n = i )}. If the Markov chain is homogeneous (that is, the
transition probability matrix @math{{\bf P}(n)} is time-independent),
we can simply write @math{{\bf P} = P_{i, j}}, where @math{P_{i, j} =
-P( X_{n+1} = j\ |\ X_n = i )} for all @math{n=0, 1, 2, @dots{}}.
+P( X_{n+1} = j\ |\ X_n = i )} for all @math{n=0, 1, @dots{}}.
The transition probability matrix @math{\bf P} must satisfy the
following two properties: (1) @math{P_{i, j} @geq{} 0} for all
@@ -80,14 +80,14 @@
@node State occupancy probabilities (DTMC)
@subsection State occupancy probabilities
-We denote with @math{{\bf \pi}(n) = (\pi_1(n), \pi_2(n), @dots{},
-\pi_N(n) )} the @emph{state occupancy probability vector} at step
+We denote with @math{{\bf \pi}(n) = \left(\pi_1(n), \pi_2(n), @dots{},
+\pi_N(n) \right)} the @emph{state occupancy probability vector} at step
@math{n}. @math{\pi_i(n)} denotes the probability that the system is
in state @math{i} at step @math{n}.
Given the transition probability matrix @math{\bf P} and the initial
-state occupancy probability vector @math{{\bf \pi}(0) = (\pi_1(0),
-\pi_2(0), @dots{}, \pi_N(0))} at step 0, the state occupancy
+state occupancy probability vector @math{{\bf \pi}(0) = \left(\pi_1(0),
+\pi_2(0), @dots{}, \pi_N(0)\right)} at step 0, the state occupancy
probability vector @math{{\bf \pi}(n)} at step @math{n} can be
computed as:
@@ -136,7 +136,7 @@
matrix @math{\bf P} and an integer @math{n @geq{} 0}, we let
@math{L_i(n)} be the the expected number of visits to state @math{i}
during the first @math{n} transitions. The vector @math{{\bf L}(n) =
-(L_1(n), L_2(n), @dots{}, L_N(n))} is defined as:
+( L_1(n), L_2(n), @dots{}, L_N(n) )} is defined as:
@iftex
@tex
@@ -239,7 +239,7 @@
A stochastic process @math{@{X(t), t @geq{} 0@}} is a continuous-time
Markov chain if, for all integers @math{n}, and for any sequence
-@math{t_0, t_1 , \ldots , t_n, t_{n+1}} such that @math{t_0 < t_1 <
+@math{t_0, t_1 , \ldots, t_n, t_{n+1}} such that @math{t_0 < t_1 <
\ldots < t_n < t_{n+1}}, we have
@iftex
@@ -333,7 +333,7 @@
Given a @math{N} state continuous-time Markov Chain with infinitesimal
generator matrix @math{\bf Q}, we define the vector @math{{\bf L}(t) =
-(L_1(t), L_2(t), \ldots L_N(t))} such that @math{L_i(t)} is the
+(L_1(t), L_2(t), \ldots, L_N(t))} such that @math{L_i(t)} is the
expected sojourn time in state @math{i} during the interval
@math{[0,t)}, assuming that the initial occupancy probability at time
0 was @math{{\bf \pi}(0)}. @math{{\bf L}(t)} can be expressed as the
Modified: trunk/octave-forge/main/queueing/doc/queueingnetworks.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueingnetworks.txi 2012-03-18 18:24:04 UTC (rev 9950)
+++ trunk/octave-forge/main/queueing/doc/queueingnetworks.txi 2012-03-18 21:03:48 UTC (rev 9951)
@@ -110,12 +110,13 @@
service, and the instant at which service finishes and the request moves
to another queue (or exits the system).
-@item P_{ij}
-Routing probability matrix. @math{{\bf P} = P_{ij}} is a @math{K \times
-K} matrix such that @math{P_{ij}} is the probability that a request
-completing service at server @math{i} will move directly to server
-@math{j}, The probability that a request leaves the system after service
-at service center @math{i} is @math{1-\sum_{j=1}^K P_{ij}}.
+@item P_{i, j}
+Routing probability matrix. @math{{\bf P} = P_{i, j}} is a @math{K
+\times K} matrix such that @math{P_{i, j}} is the probability that a
+request completing service at server @math{i} will move directly to
+server @math{j}, The probability that a request leaves the system
+after service at service center @math{i} is @math{1-\sum_{j=1}^K P_{i,
+j}}.
@item V_i
Average number of visits. @math{V_i} is the average number of visits to
@@ -172,30 +173,48 @@
@iftex
@tex
-$V_j = P_{0 j} + \sum_{i=1}^K V_i P_{i j}$
+$$ V_j = P_{0, j} + \sum_{i=1}^K V_i P_{i, j} $$
@end tex
@end iftex
@ifnottex
@example
-V == P0 + V*P;
+@group
+ K
+ ___
+ \
+V_j = P_(0, j) + > V_i P_(i, j)
+ /___
+ i=1
+@end group
@end example
@end ifnottex
-@noindent where @math{P_{0 j}} is the probability that an external
+@noindent where @math{P_{0, j}} is the probability that an external
arrival goes to service center @math{j}. If @math{\lambda_j} is the
external arrival rate to service center @math{j}, and @math{\lambda =
\sum_j \lambda_j} is the overall external arrival rate, then
-@math{P_{0 j} = \lambda_j / \lambda}.
+@math{P_{0, j} = \lambda_j / \lambda}.
For closed models, the visit ratios satisfy the following equation:
@iftex
@tex
-$V_j = \sum_{i=1}^K V_i P_{i j}$
+$$\eqalign{V_1 & = 1 \cr
+ V_j & = \sum_{i=1}^K V_i P_{i, j}} $$
@end tex
@end iftex
@ifnottex
@example
+
+V_1 = 1
+
+ K
+ ___
+ \
+V_j = > V_i P_(i, j)
+ /___
+ i=1
+
V(1) == 1 && V == V*P;
@end example
@end ifnottex
@@ -204,46 +223,46 @@
In multiple class QN models, we assume that there exist @math{C}
different classes of requests. Each request from class @math{c} spends
-on average time @math{S_{ck}} in service at service center @math{k}. For
-open models, we denote with @math{{\bf \lambda} = \lambda_{ck}} the
-arrival rates, where @math{\lambda_{ck}} is the external arrival rate of
-class @math{c} customers at service center @math{k}. For closed models,
-we denote with @math{{\bf N} = (N_1, N_2, \ldots N_C)} the population
-vector, where @math{N_c} is the number of class @math{c} requests in the
-system.
+on average time @math{S_{c, k}} in service at service center
+@math{k}. For open models, we denote with @math{{\bf \lambda} =
+\lambda_{ck}} the arrival rates, where @math{\lambda_{c, k}} is the
+external arrival rate of class @math{c} customers at service center
+@math{k}. For closed models, we denote with @math{{\bf N} = (N_1, N_2,
+\ldots, N_C)} the population vector, where @math{N_c} is the number of
+class @math{c} requests in the system.
The transition probability matrix for these kind of networks will be a
-@math{C \times K \times C \times K} matrix @math{{\bf P} =
-P_{risj}} such that @math{P_{risj}} is the probability that a
-class @math{r} request which completes service at center @math{i} will
-join server @math{j} as a class @math{s} request.
+@math{C \times K \times C \times K} matrix @math{{\bf P} = P_{r, i, s, j}}
+such that @math{P_{r, i, s, j}} is the probability that a class
+@math{r} request which completes service at center @math{i} will join
+server @math{j} as a class @math{s} request.
-Model input and outputs can be adjusted by adding additional
-indexes for the customer classes.
+Model input and outputs can be adjusted by adding additional indexes
+for the customer classes.
@noindent @strong{Model Inputs}
@table @math
-@item \lambda_{ci}
+@item \lambda_{c, i}
External arrival rate of class-@math{c} requests to service center @math{i}
@item \lambda
-Overall external arrival rate to the whole system: @math{\lambda = \sum_c \sum_i \lambda_{ci}}
+Overall external arrival rate to the whole system: @math{\lambda = \sum_c \sum_i \lambda_{c, i}}
-@item S_{ci}
-Average service time. @math{S_{ci}} is the average service time on service
-center @math{i} for class @math{c} requests.
+@item S_{c, i}
+Average service time. @math{S_{c, i}} is the average service time on
+service center @math{i} for class @math{c} requests.
-@item P_{risj}
-Routing probability matrix. @math{{\bf P} = P_{risj}} is a @math{C
-\times K \times C \times K} matrix such that @math{P_{risj}} is the
-probability that a class @math{r} request which completes service at
-server @math{i} will move to server @math{j} as a class @math{s}
+@item P_{r, i, s, j}
+Routing probability matrix. @math{{\bf P} = P_{r, i, s, j}} is a @math{C
+\times K \times C \times K} matrix such that @math{P_{r, i, s, j}} is
+the probability that a class @math{r} request which completes service
+at server @math{i} will move to server @math{j} as a class @math{s}
request.
-@item V_{ci}
-Average number of visits. @math{V_{ci}} is the average number of visits
+@item V_{c, i}
+Average number of visits. @math{V_{c, i}} is the average number of visits
of class @math{c} requests to the service center @math{i}.
@end table
@@ -252,23 +271,23 @@
@table @math
-@item U_{ci}
+@item U_{c, i}
Utilization of service center @math{i} by class @math{c} requests. The
utilization is defined as the fraction of time in which the resource is
busy (i.e., the server is processing requests).
-@item R_{ci}
+@item R_{c, i}
Average response time experienced by class @math{c} requests on service
center @math{i}. The average response time is defined as the average
time between the arrival of a customer in the queue, and the completion
of service.
-@item Q_{ci}
+@item Q_{c, i}
Average number of class @math{c} requests on service center
@math{i}. This includes both the requests in the queue, and the request
being served.
-@item X_{ci}
+@item X_{c, i}
Throughput of service center @math{i} for class @math{c} requests. The
throughput is defined as the rate of completion of class @math{c}
requests.
@@ -283,7 +302,7 @@
Utilization of service center @math{i}:
@iftex
@tex
-$U_i = \sum_{c=1}^C U_{ci}$
+$U_i = \sum_{c=1}^C U_{c, i}$
@end tex
@end iftex
@ifnottex
@@ -294,7 +313,7 @@
System response time for class @math{c} requests:
@iftex
@tex
-$R_c = \sum_{i=1}^K R_{ci} V_{ci}$
+$R_c = \sum_{i=1}^K R_{c, i} V_{c, i}$
@end tex
@end iftex
@ifnottex
@@ -305,7 +324,7 @@
Average number of class @math{c} requests in the system:
@iftex
@tex
-$Q_c = \sum_{i=1}^K Q_{ci}$
+$Q_c = \sum_{i=1}^K Q_{c, i}$
@end tex
@end iftex
@ifnottex
@@ -316,7 +335,7 @@
Class @math{c} throughput:
@iftex
@tex
-$X_c = X_{c1} / V_{c1}$
+$X_c = X_{c, 1} / V_{c, 1}$
@end tex
@end iftex
@ifnottex
@@ -325,12 +344,13 @@
@end table
-We can define the visit ratios @math{V_{sj}} for class @math{s}
+We can define the visit ratios @math{V_{s, j}} for class @math{s}
customers at service center @math{j} as follows:
@iftex
@tex
-$V_{sj} = \sum_{r=1}^C \sum_{i=1}^K V_{ri} P_{risj},\ V_{s1} = 1$
+$$ \eqalign{ V_{s, j} & = \sum_{r=1}^C \sum_{i=1}^K V_{r, i} P_{r, i, s, j} \cr
+ V_{s, 1} & = 1} $$
@end tex
@end iftex
@ifnottex
@@ -343,7 +363,7 @@
@iftex
@tex
-$V_{sj} = P_{0sj} + \sum_{r=1}^C \sum_{i=1}^K V_{ri} P_{risj}$
+$$V_{s, j} = P_{0, s, j} + \sum_{r=1}^C \sum_{i=1}^K V_{r, i} P_{r, i, s, j}$$
@end tex
@end iftex
@ifnottex
@@ -352,12 +372,12 @@
@end group
@end ifnottex
-@noindent where @math{P_{0sj}} is the probability that an external
+@noindent where @math{P_{0, s, j}} is the probability that an external
arrival goes to service center @math{j} as a class-@math{s} request.
-If @math{\lambda_{sj}} is the external arrival rate of class @math{s}
-requests to service center @math{j}, and @math{\lambda = \sum_s \sum_j
-\lambda_{sj}} is the overall external arrival rate to the whole system,
-then @math{P_{0sj} = \lambda_{sj} / \lambda}.
+If @math{\lambda_{s, j}} is the external arrival rate of class
+@math{s} requests to service center @math{j}, and @math{\lambda =
+\sum_s \sum_j \lambda_{s, j}} is the overall external arrival rate to
+the whole system, then @math{P_{0, s, j} = \lambda_{s, j} / \lambda}.
@c
@c
@@ -405,11 +425,11 @@
requests in 0.2. Note that service times are class-independent;
@item Node 2 is a @math{-/G/1}--PS node, with service times
-@math{S_{12} = 0.4} for class 1, and @math{S_{22} = 0.6} for class 2
+@math{S_{1, 2} = 0.4} for class 1, and @math{S_{2, 2} = 0.6} for class 2
requests;
@item Node 3 is a @math{-/G/\infty} node (delay center), with service
-times @math{S_{13}=1} and @math{S_{23}=2} for class 1 and 2
+times @math{S_{1, 3}=1} and @math{S_{2, 3}=2} for class 1 and 2
respectively.
@end itemize
@@ -491,14 +511,14 @@
@end itemize
We define the @emph{joint probability vector} @math{\pi(k_1, k_2,
-\ldots k_N)} as the steady-state probability that there are @math{k_i}
-requests at service center @math{i}, for all @math{i=1,2, \ldots N}.
+\ldots, k_N)} as the steady-state probability that there are @math{k_i}
+requests at service center @math{i}, for all @math{i=1, 2, \ldots, N}.
Jackson networks have the property that the joint probability is the
product of the marginal probabilities @math{\pi_i}:
@iftex
@tex
-$$ \pi(k_1, k_2, \ldots k_N) = \prod_{i=1}^N \pi_i(k_i) $$
+$$ \pi(k_1, k_2, \ldots, k_N) = \prod_{i=1}^N \pi_i(k_i) $$
@end tex
@end iftex
@ifnottex
@@ -532,7 +552,7 @@
@iftex
@tex
-$$ \pi(k_1, k_2, \ldots k_K) = {1 \over G(N)} \prod_{i=1}^N F_i(k_i) $$
+$$ \pi(k_1, k_2, \ldots, k_K) = {1 \over G(N)} \prod_{i=1}^N F_i(k_i) $$
@end tex
@end iftex
@ifnottex
@@ -544,14 +564,14 @@
@end example
@end ifnottex
-Here @math{\pi(k_1, k_2, \ldots k_K)} is the joint probability of
-having @math{k_i} requests at node @math{i}, for all @math{i=1,2,
-\ldots K}.
+Here @math{\pi(k_1, k_2, \ldots, k_K)} is the joint probability of
+having @math{k_i} requests at node @math{i}, for all @math{i=1, 2,
+\ldots, K}.
The @emph{convolution algorithms} computes the normalization constants
-@math{G = (G(0), G(1), \ldots G(N))} for single-class, closed networks
+@math{{\bf G} = \left(G(0), G(1), \ldots, G(N)\right)} for single-class, closed networks
with @math{N} requests. The normalization constants are returned as
-vector @code{@var{G}=[@var{G}(1), @var{G}(2), ... @var{G}(N+1)]} where
+vector @code{@var{G}=[@var{G}(1), @var{G}(2), @dots{} @var{G}(N+1)]} where
@code{@var{G}(i+1)} is the value of @math{G(i)} (remember that Octave
uses 1-base vectors). The normalization constant can be used to
compute all performance measures of interest (utilization, average
@@ -574,14 +594,14 @@
The normalization constant @math{G} can be used to compute the
steady-state probabilities for a closed single class product-form
Queueing Network with @math{K} nodes. Let @code{@var{k}=[@math{k_1,
-k_2, @dots{} k_K}]} be a valid population vector. Then, the
+k_2, @dots{}, k_K}]} be a valid population vector. Then, the
steady-state probability @code{@var{p}(i)} to have @code{@var{k}(i)}
requests at service center @math{i} can be computed as:
@iftex
@tex
$$
-p_i(k_i) = {(V_i S_i)^{k_i} \over G(K)} \left(G(K-k_i) - V_i S_i G(K-k_i-1)\right), \quad i=1,2, \ldots K
+p_i(k_i) = {(V_i S_i)^{k_i} \over G(K)} \left(G(K-k_i) - V_i S_i G(K-k_i-1)\right), \quad i=1, 2, \ldots, K
$$
@end tex
@end iftex
@@ -841,7 +861,7 @@
@noindent @strong{NOTE}
Given a network with @math{K} service centers, @math{C} job classes and
-population vector @math{{\bf N}=(N_1, N_2, \ldots N_C)}, the MVA
+population vector @math{{\bf N}=(N_1, N_2, \ldots, N_C)}, the MVA
algorithm requires space @math{O(C \prod_i (N_i + 1))}. The time
complexity is @math{O(CK\prod_i (N_i + 1))}. This implementation is
slightly more space-efficient (see details in the code). While the space
@@ -1085,7 +1105,7 @@
@iftex
@tex
-$V_j = P_{0 j} + \sum_{i=1}^K V_i P_{i j}$
+$$V_j = P_{0, j} + \sum_{i=1}^K V_i P_{i, j}$$
@end tex
@end iftex
@ifnottex
@@ -1094,17 +1114,18 @@
@end example
@end ifnottex
-@noindent where @math{P_{0 j}} is the probability that an external
+@noindent where @math{P_{0, j}} is the probability that an external
arrival goes to service center @math{j}. If @math{\lambda_j} is the
external arrival rate to service center @math{j}, and @math{\lambda =
\sum_j \lambda_j} is the overall external arrival rate, then
-@math{P_{0 j} = \lambda_j / \lambda}.
+@math{P_{0, j} = \lambda_j / \lambda}.
For closed networks, the visit ratios satisfy the following equation:
@iftex
@tex
-$V_j = \sum_{i=1}^K V_i P_{i j},\ V_1 = 1$
+$$\eqalign{ V_j & = \sum_{i=1}^K V_i P_{i, j} \cr
+ V_1 & = 1 }$$
@end tex
@end iftex
@ifnottex
@@ -1114,12 +1135,13 @@
@end ifnottex
The definitions above can be extended to multiple class networks as
-follows. We define the visit ratios @math{V_{sj}} for class @math{s}
+follows. We define the visit ratios @math{V_{s, j}} for class @math{s}
customers at service center @math{j} as follows:
@iftex
@tex
-$V_{sj} = \sum_{r=1}^C \sum_{i=1}^K V_{ri} P_{risj},\ V_{s1} = 1$
+$$\eqalign{ V_{s, j} & = \sum_{r=1}^C \sum_{i=1}^K V_{r, i} P_{r, i, s, j} \cr
+ V_{s, 1} & = 1 }$$
@end tex
@end iftex
@ifnottex
@@ -1133,7 +1155,7 @@
@iftex
@tex
-$V_{sj} = P_{0sj} + \sum_{r=1}^C \sum_{i=1}^K V_{ri} P_{risj}$
+$$V_{s, j} = P_{0, s, j} + \sum_{r=1}^C \sum_{i=1}^K V_{r, i} P_{r, i, s, j}$$
@end tex
@end iftex
@ifnottex
@@ -1142,12 +1164,12 @@
@end group
@end ifnottex
-@noindent where @math{P_{0sj}} is the probability that an external
+@noindent where @math{P_{0, s, j}} is the probability that an external
arrival goes to service center @math{j} as a class-@math{s} request.
-If @math{\lambda_{sj}} is the external arrival rate of class @math{s}
+If @math{\lambda_{s, j}} is the external arrival rate of class @math{s}
requests to service center @math{j}, and @math{\lambda = \sum_s \sum_j
-\lambda_{sj}} is the overall external arrival rate to the whole system,
-then @math{P_{0sj} = \lambda_{sj} / \lambda}.
+\lambda_{s, j}} is the overall external arrival rate to the whole system,
+then @math{P_{0, s, j} = \lambda_{s, j} / \lambda}.
@DOCSTRING(qnvisits)
@@ -1172,7 +1194,7 @@
80-355.pdf}
Note that the slightly different problem of generating all tuples
-@math{k_1, k_2, \ldots k_N} such that @math{\sum_i k_i = k} and
+@math{k_1, k_2, \ldots, k_N} such that @math{\sum_i k_i = k} and
@math{k_i} are nonnegative integers, for some fixed integer @math{k
@geq{} 0} has been described in S. Santini, @cite{Computing the
Indices for a Complex Summation}, unpublished report, available at
Modified: trunk/octave-forge/main/queueing/doc/references.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/references.txi 2012-03-18 18:24:04 UTC (rev 9950)
+++ trunk/octave-forge/main/queueing/doc/references.txi 2012-03-18 21:03:48 UTC (rev 9951)
@@ -27,14 +27,17 @@
@item [Aky88]
Ian F. Akyildiz, @cite{Mean Value Analysis for Blocking Queueing
Networks}, IEEE Transactions on Software Engineering, vol. 14, n. 2,
-april 1988, pp. 418--428. @url{http://dx.doi.org/10.1109/32.4663}
+april 1988, pp. 418--428. DOI @uref{http://dx.doi.org/10.1109/32.4663, 10.1109/32.4663}
@item [Bar79]
Y. Bard, @cite{Some Extensions to Multiclass Queueing Network Analysis},
proc. 4th Int. Symp. on Modelling and Performance Evaluation of
Computer Systems, feb. 1979, pp. 51--62.
-@item [RGMT98]
+@item [BCMP75]
+Forest Baskett, K. Mani Chandy, Richard R. Muntz, and Fernando G. Palacios. 1975. @cite{Open, Closed, and Mixed Networks of Queues with Different Classes of Customers}. J. ACM 22, 2 (April 1975), 248—260, DOI @uref{http://doi.acm.org/10.1145/321879.321887, 10.1145/321879.321887}
+
+@item [BGMT98]
G. Bolch, S. Greiner, H. de Meer and
K. Trivedi, @cite{Queueing Networks and Markov Chains: Modeling and
Performance Evaluation with Computer Science Applications}, Wiley,
@@ -44,20 +47,25 @@
Jeffrey P. Buzen, @cite{Computational Algorithms for Closed Queueing
Networks with Exponential Servers}, Communications of the ACM, volume
16, number 9, september 1973,
-pp. 527--531. @url{http://doi.acm.org/10.1145/362342.362345}
+pp. 527--531. DOI @uref{http://doi.acm.org/10.1145/362342.362345, 10.1145/362342.362345}
@item [CMS08]
G. Casale, R. R. Muntz, G. Serazzi,
@cite{Geometric Bounds: a Non-Iterative Analysis Technique for Closed
Queueing Networks}, IEEE Transactions on Computers, 57(6):780-794,
-June 2008. @url{http://doi.ieeecomputersociety.org/10.1109/TC.2008.37}
+June 2008. DOI @uref{http://doi.ieeecomputersociety.org/10.1109/TC.2008.37, 10.1109/TC.2008.37}
@item [GrSn97]
-Charles M. Grinstead, J. Laurie Snell, (July 1997). Introduction to
-Probability. American Mathematical Society. ISBN 978-0821807491
+Charles M. Grinstead, J. Laurie Snell, (July 1997). @cite{Introduction
+to Probability}. American Mathematical Society. ISBN 978-0821807491;
+this excellent textbook is @uref{http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf, available in PDF format}
+and can be used under the terms of the @uref{http://www.gnu.org/copyleft/fdl.html, GNU Free Documentation License (FDL)}
+@item [Jac04]
+James R. Jackson, @cite{Jobshop-Like Queueing Systems}, Vol. 50, No. 12, Ten Most Influential Titles of "Management Science's" First Fifty Years (Dec., 2004), pp. 1796-1802, @uref{http://www.jstor.org/stable/30046149, available online}
+
@item [Jai91]
-R. Jain , @cite{The Art of Computer Systems Performance Analysis},
+R. Jain, @cite{The Art of Computer Systems Performance Analysis},
Wiley, 1991, p. 577.
@item [HsLa87]
@@ -69,7 +77,7 @@
Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C.
Sevcik, @cite{Quantitative System Performance: Computer System
Analysis Using Queueing Network Models}, Prentice Hall,
-1984. @url{http://www.cs.washington.edu/homes/lazowska/qsp/}.
+1984. @uref{http://www.cs.washington.edu/homes/lazowska/qsp/, available online}.
@item [ReKo76]
M. Reiser, H. Kobayashi, @cite{On The Convolution Algorithm for
@@ -77,31 +85,33 @@
SIGMETRICS Conference on Computer Performance Modeling Measurement and
Evaluation (Cambridge, Massachusetts, United States, March 29--31,
1976). SIGMETRICS '76. ACM, New York, NY,
-pp. 109--117. @url{http://doi.acm.org/10.1145/800200.806187}
+pp. 109--117. DOI @uref{http://doi.acm.org/10.1145/800200.806187, 10.1145/800200.806187}
@item [ReLa80]
M. Reiser and S. S. Lavenberg, @cite{Mean-Value Analysis of Closed
Multichain Queuing Networks}, Journal of the ACM, vol. 27, n. 2, April
-1980, pp. 313--322. @url{http://doi.acm.org/10.1145/322186.322195}
+1980, pp. 313--322. DOI @uref{http://doi.acm.org/10.1145/322186.322195, 10.1145/322186.322195}
+@item [Sch79]
+P. Schweitzer, @cite{Approximate Analysis of Multiclass Closed Networks of
+Queues}, Proc. Int. Conf. on Stochastic Control and Optimization, jun
+1979, pp. 25—29
+
@item [Sch81]
Herb Schwetman, @cite{Some Computational
-Aspects of Queueing Network Models}, Technical Report CSD-TR-354,
+Aspects of Queueing Network Models}, @uref{http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf, Technical Report CSD-TR-354},
Department of Computer Sciences, Purdue University, feb, 1981
(revised).
-@url{http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf}
@item [Sch82]
Herb Schwetman, @cite{Implementing the Mean Value Algorithm for the
-Solution of Queueing Network Models}, Technical Report CSD-TR-355,
-Department of Computer Sciences, Purdue University, feb 15, 1982,
-available at
-@url{http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf}
+Solution of Queueing Network Models}, @uref{http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf, Technical Report CSD-TR-355},
+Department of Computer Sciences, Purdue University, feb 15, 1982.
@item [ZaWo81]
Zahorjan, J. and Wong, E. @cite{The solution of separable queueing
network models using mean value analysis}. SIGMETRICS
Perform. Eval. Rev. 10, 3 (Sep. 1981), 80-85. DOI
-@url{http://doi.acm.org/10.1145/1010629.805477}
+DOI @uref{http://doi.acm.org/10.1145/1010629.805477, 10.1145/1010629.805477}
@end table
Modified: trunk/octave-forge/main/queueing/inst/dtmc_taexps.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc_taexps.m 2012-03-18 18:24:04 UTC (rev 9950)
+++ trunk/octave-forge/main/queueing/inst/dtmc_taexps.m 2012-03-18 21:03:48 UTC (rev 9951)
@@ -35,7 +35,7 @@
## Infinitesimal generator matrix. @code{@var{Q}(i,j)} is the transition
## rate from state @math{i} to state @math{j},
## @math{1 @leq{} i \neq j @leq{} N}. The
-## matrix @var{Q} must also satisfy the condition @math{\sum_{j=1}^N Q_{ij} = 0}
+## matrix @var{Q} must also satisfy the condition @math{\sum_{j=1}^N Q_{i, j} = 0}
##
## @item t
## Time. If omitted, the results are computed until absorption.
Modified: trunk/octave-forge/main/queueing/inst/qnmarkov.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/qnmarkov.m 2012-03-18 18:24:04 UTC (rev 9950)
+++ trunk/octave-forge/main/queueing/inst/qnmarkov.m 2012-03-18 21:03:48 UTC (rev 9951)
@@ -54,14 +54,14 @@
##
## @item Average service times are load-independent.
##
-## @item @math{P_{ij}} is the probability that requests completing
+## @item @math{P_{i, j}} is the probability that requests completing
## execution at center @math{i} are transferred to
## center @math{j}, @math{i \neq j}. For open networks, a request may leave the system
-## from any node @math{i} with probability @math{1-\sum_j P_{ij}}.
+## from any node @math{i} with probability @math{1-\sum_j P_{i, j}}.
##
## @item Blocking type is Repetitive-Service (RS). Service
## center @math{j} is @emph{saturated} if the number of requests is equal
-## to its capacity @code{C_j}. Under the RS blocking discipline,
+## to its capacity @math{C_j}. Under the RS blocking discipline,
## a request completing service at center @math{i} which is being
## transferred to a saturated server @math{j} is put back at the end of
## the queue of @math{i} and will receive service again. Center @math{i}
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
|
From: <mma...@us...> - 2012-03-18 18:24:10
|
Revision: 9950
http://octave.svn.sourceforge.net/octave/?rev=9950&view=rev
Author: mmarzolla
Date: 2012-03-18 18:24:04 +0000 (Sun, 18 Mar 2012)
Log Message:
-----------
fixed typos in documentation
Modified Paths:
--------------
trunk/octave-forge/main/queueing/doc/markovchains.txi
trunk/octave-forge/main/queueing/inst/ctmc.m
trunk/octave-forge/main/queueing/inst/dtmc.m
trunk/octave-forge/main/queueing/inst/dtmc_exps.m
Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-18 16:09:48 UTC (rev 9949)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi 2012-03-18 18:24:04 UTC (rev 9950)
@@ -35,7 +35,7 @@
@dots{}}. The sequence @math{X_0, X_1, @dots{}, X_n, @dots{}} is a
@emph{stochastic process} with discrete time @math{0, 1, 2,
@dots{}}. A @emph{Markov chain} is a stochastic process @math{@{X_n,
-n=0, 1, 2, @dots{}@}} which satisfies the following Marrkov property:
+n=0, 1, 2, @dots{}@}} which satisfies the following Markov property:
@iftex
@tex
@@ -46,7 +46,7 @@
@math{P(X_{n+1} = x_{n+1} | X_n = x_n, X_{n-1} = x_{n-1}, ..., X_0 = x_0) = P(X_{n+1} = x_{n+1} | X_n = x_n)}
@end ifnottex
-@noindent which means that the probability that the system is in
+@noindent which means that the probability that the system is in
a particular state at time @math{n+1} only depends on the state the
system was at time @math{n}.
@@ -60,7 +60,7 @@
The transition probability matrix @math{\bf P} must satisfy the
following two properties: (1) @math{P_{i, j} @geq{} 0} for all
-@math{i, j}, and (2) @math{\sum_{j=1}^N P_{i,j} = 1}.
+@math{i, j}, and (2) @math{\sum_{j=1}^N P_{i,j} = 1}.
@c
@DOCSTRING(dtmc_check_P)
@@ -70,8 +70,8 @@
* Birth-death process (DTMC)::
* Expected number of visits (DTMC)::
* Time-averaged expected sojourn times (DTMC)::
+* Mean time to absorption (DTMC)::
* First passage times (DTMC)::
-* Mean time to absorption (DTMC)::
@end menu
@c
@@ -134,7 +134,7 @@
Given a @math{N} state discrete-time Markov chain with transition
matrix @math{\bf P} and an integer @math{n @geq{} 0}, we let
-@math{L-I(n)} be the the expected number of visits to state @math{i}
+@math{L_i(n)} be the the expected number of visits to state @math{i}
during the first @math{n} transitions. The vector @math{{\bf L}(n) =
(L_1(n), L_2(n), @dots{}, L_N(n))} is defined as:
@@ -156,8 +156,8 @@
@end example
@end ifnottex
-@noindent where @math{{\bf \pi}(i) = {\bf \pi}(0){\bf P}^i} is the state occupancy probability
-after @math{i} transitions.
+@noindent where @math{{\bf \pi}(i) = {\bf \pi}(0){\bf P}^i} is the state
+occupancy probability after @math{i} transitions.
If @math{\bf P} is absorbing, we can rearrange the states to rewrite
@math{\bf P} as:
@@ -186,7 +186,7 @@
number of times that the process is in the @math{j}-th transient state
if it is started in the @math{i}-th transient state. If we reshape
@math{\bf N} to the size of @math{\bf P} (filling missing entries with
-zeros), we have that, for abrosbing chains @math{{\bf L} = {\bf
+zeros), we have that, for absorbing chains @math{{\bf L} = {\bf
\pi}(0){\bf N}}.
@DOCSTRING(dtmc_exps)
@@ -198,17 +198,23 @@
@DOCSTRING(dtmc_taexps)
@c
+@node Mean time to absorption (DTMC)
+@subsection Mean Time to Absorption
+
+@DOCSTRING(dtmc_mtta)
+
+@c
@node First passage times (DTMC)
@subsection First Passage Times
-The First Passage Time @math{M_{i j}} is defined as the average
+The First Passage Time @math{M_{i, j}} is defined as the average
number of transitions needed to visit state @math{j} for the first
time, starting from state @math{i}. Matrix @math{\bf M} satisfies the
property that
@iftex
@tex
-$$ M_{i j} = 1 + \sum_{k \neq j} P_{i k} M_{k j}$$
+$$ M_{i, j} = 1 + \sum_{k \neq j} P_{i, k} M_{k, j}$$
@end tex
@end iftex
@ifnottex
@@ -217,24 +223,17 @@
___
\
M_ij = 1 + > P_ij * M_kj
- /___
- k!=j
+ /___
+ k!=j
@end group
@end example
@end ifnottex
-@c
@DOCSTRING(dtmc_fpt)
@c
-@node Mean time to absorption (DTMC)
-@subsection Mean Time to Absorption
-
-@DOCSTRING(dtmc_mtta)
-
@c
@c
-@c
@node Continuous-Time Markov Chains
@section Continuous-Time Markov Chains
@@ -257,7 +256,7 @@
that for each @math{i \neq j}, @math{Q_{i, j}} is the transition rate
from state @math{i} to state @math{j}. The elements @math{Q_{i, i}}
must be defined in such a way that the infinitesimal generator matrix
-@math{\bf Q} satisfies the property @math{\sum_{j=1}^N Q_{i,j} = 0}.
+@math{\bf Q} satisfies the property @math{\sum_{j=1}^N Q_{i, j} = 0}.
@DOCSTRING(ctmc_check_Q)
@@ -301,7 +300,7 @@
@emph{stationary state occupancy probability} @math{{\bf \pi} =
\lim_{t \rightarrow +\infty} {\bf \pi}(t)}, which is independent from
the initial state occupancy @math{{\bf \pi}(0)}. The stationary state
-occupancy probability vector @math{\bf \pi} satisfies
+occupancy probability vector @math{\bf \pi} satisfies
@math{{\bf \pi} {\bf Q} = {\bf 0}} and @math{\sum_{i=1}^N \pi_i = 1}.
@DOCSTRING(ctmc)
@@ -337,8 +336,8 @@
(L_1(t), L_2(t), \ldots L_N(t))} such that @math{L_i(t)} is the
expected sojourn time in state @math{i} during the interval
@math{[0,t)}, assuming that the initial occupancy probability at time
-0 was @math{{\bf \pi}(0)}. @math{{\bf L}(t)} is the solution of
-the following differential equation:
+0 was @math{{\bf \pi}(0)}. @math{{\bf L}(t)} can be expressed as the
+solution of the following differential equation:
@iftex
@tex
@@ -367,14 +366,15 @@
@example
@group
/ t
-L(t) = | pi(u) du
- / u=0
+L(t) = | pi(u) du
+ / 0
@end group
@end example
@end ifnottex
@noindent where @math{{\bf \pi}(t) = {\bf \pi}(0) \exp({\bf Q}t)} is
-the state occupancy probability at time @math{t}.
+the state occupancy probability at time @math{t}; @math{\exp({\bf A})}
+is the matrix exponential of @math{\bf A}.
@DOCSTRING(ctmc_exps)
@@ -384,7 +384,7 @@
rate from state @math{i} to state @math{i+1} is @math{\lambda_i = i
\lambda} (@math{i=1, 2, 3}), with @math{\lambda = 0.5}. The following
code computes the expected sojourn time in state @math{i},
-given the initial occupancy probability @math{{\bf \pi}_0=(1,0,0,0)}.
+given the initial occupancy probability @math{{\bf \pi}_0=(1,0,0,0)}.
@example
@group
Modified: trunk/octave-forge/main/queueing/inst/ctmc.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc.m 2012-03-18 16:09:48 UTC (rev 9949)
+++ trunk/octave-forge/main/queueing/inst/ctmc.m 2012-03-18 18:24:04 UTC (rev 9950)
@@ -41,7 +41,7 @@
## Infinitesimal generator matrix. @var{Q} is a @math{N \times N} square
## matrix where @code{@var{Q}(i,j)} is the transition rate from state
## @math{i} to state @math{j}, for @math{1 @leq{} i \neq j @leq{} N}.
-## Transition rates must be nonnegative, and @math{\sum_{j=1}^N Q_{i j} = 0}
+## Transition rates must be nonnegative, and @math{\sum_{j=1}^N Q_{i, j} = 0}
##
## @item t
## Time at which to compute the transient probability
Modified: trunk/octave-forge/main/queueing/inst/dtmc.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc.m 2012-03-18 16:09:48 UTC (rev 9949)
+++ trunk/octave-forge/main/queueing/inst/dtmc.m 2012-03-18 18:24:04 UTC (rev 9950)
@@ -42,7 +42,7 @@
## @item P
## @code{@var{P}(i,j)} is the transition probability from state @math{i}
## to state @math{j}. @var{P} must be an irreducible stochastic matrix,
-## which means that the sum of each row must be 1 (@math{\sum_{j=1}^N P_{i j} = 1}), and the rank of
+## which means that the sum of each row must be 1 (@math{\sum_{j=1}^N P_{i, j} = 1}), and the rank of
## @var{P} must be equal to its dimension.
##
## @item n
Modified: trunk/octave-forge/main/queueing/inst/dtmc_exps.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc_exps.m 2012-03-18 16:09:48 UTC (rev 9949)
+++ trunk/octave-forge/main/queueing/inst/dtmc_exps.m 2012-03-18 18:24:04 UTC (rev 9950)
@@ -34,12 +34,12 @@
##
## @item n
## Number of steps during which the expected number of visits are
-## computed (@math{@var{n} @geq{} 0}). If @code{@var{n}=0}, simply
-## returns @var{p0}. If @code{@var{n} > 0}, returns the expected number
-## of visits after exactly @var{n} transitions.
+## computed (@math{@var{n} @geq{} 0}). If @code{@var{n}=0}, returns
+## @var{p0}. If @code{@var{n} > 0}, returns the expected number of
+## visits after exactly @var{n} transitions.
##
## @item p0
-## Initial state occupancy probability
+## Initial state occupancy probability.
##
## @end table
##
@@ -51,7 +51,8 @@
## When called with two arguments, @code{@var{L}(i)} is the expected
## number of visits to transient state @math{i} before absorption. When
## called with three arguments, @code{@var{L}(i)} is the expected number
-## of visits to state @math{i} during the first @var{n} transitions.
+## of visits to state @math{i} during the first @var{n} transitions,
+## given initial occupancy probability @var{p0}.
##
## @end table
##
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|
|
From: <prn...@us...> - 2012-03-18 16:09:55
|
Revision: 9949
http://octave.svn.sourceforge.net/octave/?rev=9949&view=rev
Author: prnienhuis
Date: 2012-03-18 16:09:48 +0000 (Sun, 18 Mar 2012)
Log Message:
-----------
Texinfo header fixes (get_first_help_sentence compatibility)
Modified Paths:
--------------
trunk/octave-forge/main/io/inst/io_ods_testscript.m
trunk/octave-forge/main/io/inst/io_xls_testscript.m
trunk/octave-forge/main/io/inst/object2json.m
trunk/octave-forge/main/io/inst/odsfinfo.m
Modified: trunk/octave-forge/main/io/inst/io_ods_testscript.m
===================================================================
--- trunk/octave-forge/main/io/inst/io_ods_testscript.m 2012-03-18 16:05:16 UTC (rev 9948)
+++ trunk/octave-forge/main/io/inst/io_ods_testscript.m 2012-03-18 16:09:48 UTC (rev 9949)
@@ -14,7 +14,7 @@
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
-## Check proper operation of ODS spreadsheet scripts
+## (Internal function) Check proper operation of ODS spreadsheet scripts.
## Before running, a character variable 'intf' should be initialized with
## a value of 'otk', 'jod', or 'uno'.
Modified: trunk/octave-forge/main/io/inst/io_xls_testscript.m
===================================================================
--- trunk/octave-forge/main/io/inst/io_xls_testscript.m 2012-03-18 16:05:16 UTC (rev 9948)
+++ trunk/octave-forge/main/io/inst/io_xls_testscript.m 2012-03-18 16:09:48 UTC (rev 9949)
@@ -14,7 +14,7 @@
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
-## Check proper operation of XLS spreadsheet scripts.
+## (Internal function) Check proper operation of XLS spreadsheet scripts.
## Before running, a character variable 'intf' should be initialized with
## a value of 'com', 'poi', 'jxl', 'oxs', or 'uno'.
Modified: trunk/octave-forge/main/io/inst/object2json.m
===================================================================
--- trunk/octave-forge/main/io/inst/object2json.m 2012-03-18 16:05:16 UTC (rev 9948)
+++ trunk/octave-forge/main/io/inst/object2json.m 2012-03-18 16:09:48 UTC (rev 9949)
@@ -23,8 +23,8 @@
function json = object2json (object)
% function json = object2json (object)
- % This function returns a valid json string that will describe object
- % The string will be in a compact form (i.e. no spaces or line breaks)
+ % Returns a valid json string that will describe object; the string will
+ % be in a compact form (no spaces or line breaks).
%
% It will map simple octave values this way:
% function handles: string with the name of the function
Modified: trunk/octave-forge/main/io/inst/odsfinfo.m
===================================================================
--- trunk/octave-forge/main/io/inst/odsfinfo.m 2012-03-18 16:05:16 UTC (rev 9948)
+++ trunk/octave-forge/main/io/inst/odsfinfo.m 2012-03-18 16:09:48 UTC (rev 9949)
@@ -17,7 +17,7 @@
## -*- texinfo -*-
## @deftypefn {Function File} [@var{filetype}] = odsfinfo (@var{filename} [, @var{reqintf}])
## @deftypefnx {Function File} [@var{filetype}, @var{sh_names}] = odsfinfo (@var{filename} [, @var{reqintf}])
-## Query an OpenOffice_org spreadsheet file @var{filename} (with .ods
+## Query an OpenOffice_org spreadsheet file @var{filename} (with ods
## suffix) for some info about its contents.
##
## If @var{filename} is a recognizable OpenOffice.org spreadsheet file,
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